Diese erste, umfassende Darstellung von Kants Philosophie der Mathematik unternimmt es, die Aussagen Kants über Mathematik im Kontext seiner jeweiligen philosophischen Problemkonstellation zu verorten. Darüber hinaus werden die Ergebnisse dieser Zuweisungen einer systematischen Evaluation unterworfen. Der Befund: Kants Mathematikbegriff ist durch Prämissen geprägt, die sich aus seinen generellen philosophischen Einstellungen ergeben. Es sind also nicht so sehr die immanenten Probleme der Mathematik, die Kants Bild vom Wesen des Mathematischen bestimmten, sondern vielmehr die systematischen Probleme der Philosophie, die ihn zu einer (...) Auseinandersetzung mit den epistemischen und methodologischen Aspekten der Mathematik nötigten. (shrink)

Diese Studie versucht, die Grundlinien der kantischen Mathematiktheorie zu entwickeln. Es zeigt sich, dass das Problem des "epistemischen Bezugs" zu mathematischen Gegenständen im Mittelpunkt steht. Kant entwickelt hierzu zwei Strategien: unter der Voraussetzung, dass mathematische Erkenntnis "Erkenntnis in concreto", also anschaulich ist, zeigt er 1762, dass diese sich von der empirischen in der Methode der Begriffsbildung unterscheidet. Dies führt auf einen "schwachen" Aprioritätsbegriff. 1770 entwickelt Kant eine anspruchsvollere Theorie: er zeigt, dass die Anschaulichkeit und Apriorität mathematischer Erkenntnis uns nötigen, ein (...) entsprechendes ontologisches Substrat zu fordern, dass er mit Raum und Zeit identifiziert. Diese Strategie wird hier als unbefriedigend kritisiert, und es wird vorgeschlagen, die "schwächere" Konzeption von 1762 stärker zu akzentuieren: mathematische Begriffe können sich auf empirische Anschauungen beziehen; der Bezug auf reine Anschauungen ist dagegen explanatorisch überflüssig. (shrink)

Zu den interessantesten, aber auch umstrittensten Abschnitten der „Kritik der reinen Vernunft“ zählt ohne Zweifel die transzendentale Ästhetik. Kant präsentiert hier eine völlig neuartige Theorie von Raum und Zeit, wonach diese „reine Anschauungen“ sind und als solche keine „transzendentale Realität“ besitzen. Dennoch – oder gerade deshalb – sollen die mathematischen Wahrheiten mit apodiktischer Sicherheit auf die raumzeitlich erscheinende Welt applizierbar sein. Kant behauptet sogar, dass nur seine Theorie von Raum und Zeit als reinen Anschauungen die Anwendbarkeit von Mathematik verständlich macht. (...) Wer sich also für Kants Mathematiktheorie interessiert, der muss sich auch mit Kants Theorie von Raum und Zeit auseinandersetzen. (shrink)

Zoroastrianism, one of the three recognized religious minorities in the Islamic Republic, can claim a specific linkage with Iran since the Avestan Vendidād and its other primary religious documents were written in Iranian languages and its history has for the most part unfolded in Iran. The term Aryan is used in inscriptions by the Achaemenian king Darius I as a way to gloss the name of the deity Ahura Mazdā. In the Sasanian period, Iran became the name of the (...) empire. Zoroastrian literature written under Islamic rule, reaffirms the idea of a unity between kingship and religion, but transposes its realization into the eschatological future. After centuries of decline and discrimination, twentieth-century modernization entailed the prospect of societal reintegration for Zoroastrians; an unachieved hope under the Pahlavis, this prospect has become even more remote under the political conditions imposed by the Islamic Republic, where Zoroastrians now use the vocabulary of martyrdom to express their commitment to their homeland. (shrink)

The author examines john locke's arguments concerning the existence and binding force of natural law. (staff).

... V The Foundations of Mathematics Braithwaite VI Logical Studies von Wright VII A Treatise on Induction and Probability von Wright VIII An Examination of ...

Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents have (...) at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio.We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933. (shrink)

ZusammenfassungDas Axiomensystem der ebenen projektiven Geometrie ist dual in dem Sinne, dass es bei Vertauschung der Begriffe « Punkt » und « Gerade » in sich übergeht. Daraus folgt, dass mit jedem Satz auch der duale Satz aus den Axiomen beweisbar ist. Dagegen kann aus der Dualität des Axiomensystems nicht geschlossen werden, dass in einem Modell mit jedem Satz auch der duale Satz gilt; noch weniger folgt, dass ein Modell eine eineindeutige Abbildung zulässt, welche Punkte and Geraden unter Erhaltung der (...) Inzidenz vertauscht. Im Falle der projektiven Geometrie sind solche Modelle bekannt; für die einfache Typentheorie wird gezeigt, dassa die Existenz solcher Modelle äquivalent ist mit der Widerspruchsfreiheit des Systems « New Foundations ».Zusatz. Der folgende Satz beantwortet die beiden in der Arbeit aufgeworfenen Fragen: Eine vollständige Theorie mit einem Automorphismus hat ein Modell, welches einen entsprechenden Automorphismus zulässt. Insbesondere ist somit NF widerspruchsfrei, wenn die einfache Typentheorie mit den zusätzlichen Axiomen S ≡ S* widerspruchsfrei ist.RésuméLe système d'axiomes de la géométrie projective plane est dualistique dans le sens qu'il se transforme en lui‐même si I'on y échange les notions « points » et « droite ». Cette dualité entraîne un parallélisme des théorémes et de leurs démonstrations. Par contre, la dualité d'un système d'axiomes ne nous permet pas de conclure au parallélisme des énoncés qui soient vrais dans un modéle donné du systéme; moins encore peut‐on insérer I'existence d'une transformation biunivoque échangeant points et droites et conservant la relation d'incidence. Pour la géométric projective, de tels modèles sont bien connus; pour la théorie simple des types, I'existence d'un tel modèle est équivalent a la cohérence du système « New Foundations ».Remarque. Le théoréme suivant résout les deux problèmes proposés dans le travail: Toute théorie complète admettant un automorphisme possède un modèle admettant un automorphisme correspondant. NF est par conséquent cohérent si la théorie simple des types avec les axiomes supplémentaires S ≡ S * est cohérente.The axiom system of plane projective geometry is dual in the sense that it is transformed into itself by exchange of the notions « point » and « line.» It follows that for every theorem the dual sentence is also a theorem. However, from the duality of the axiom system one cannot conclude that in a model the truth of a sentence implies that of the dual sentence; even less can one conclude that each model admits a 1‐1‐transformation interchanging points and lines and preserving the incidence relation. For projective geometry, models of this kind are well known. For the simple theory of types it is shown that the existence of such models is equivalent to the consistency of « New Foundations. »Additional remark. The following theorem answers both of the questions proposed in the paper: If it is complete, then a theory with an automorphism has a model with a corresponding automorphism. NF is therefore consistent if simple theory of type with the additional axioms S ≡ S* is consistent. (shrink)

Betr. u.a. Erasmus und die Reformation in Basel.

INTRODUCTION TO THE THIRD EDITION: FROM VALUE THEORY TO PRAXEOLOGY Ludwig von Mises (1881–1973) is arguably the most important economist of the twentieth ...

ABSTRACTAchievements are among the things that make a life good. Assessing the plausibility of this intuitive claim requires an account of the nature of achievements. One necessary condition for achievement appears to be that the achieving agent acted competently, i.e. was not just lucky. I begin by critically assessing existing accounts of anti-luck conditions for achievements in both the ethics and epistemology literature. My own proposal is that a goal is reached competently, only if the actions of the would-be-achiever make (...) success likely, and that this is the reason why she acts that way. (shrink)

Why is it so plausible that business organisations in contemporary society use values in their communication? In order to answer this question, a sociological, system theoretical approach is applied which approaches values not pre-empirically as invisible drivers for action but as observable semantics that form organisational behaviour. In terms of empirical material, it will be shown that business organisations resort to a communication of values whenever uncertainty or complexity is very high. Inevitably, value semantics are applied in organisations first when (...) the speakers are uncertain about which stakeholders to whom they have to address or when different stakeholder groups have to be addressed simultaneously ; second, when the identity of the organisation has to be described; and third, when future strategic options that cannot be expressed by quantitative terms have to be communicated. Values accordingly play a role in organisational practice when certain aspects are indeterminate. Therefore, they are a means for organisations to communicate under fuzzy circumstances. On the basis of these findings, new approaches to value management can now be formulated. (shrink)

Now you can learn from the original, most important source for magic in the Western world that has ever been published, when you get Agrippa'sThree Books of Occult Philosophy. This massive volume was originally published in 1531, and occultists have been drawing on it ever since. Now, Llewellyn is proud to produce the first complete reprint of the original English translation in the last 500 years. Donald Tyson edited this work and removed the hundreds of errors that appeared in the (...) original translation. He also fully annotated the work, to make it understandableand usableby people today. ·Discover what the Renaissance scholar knew about astrology, medicine, history, herbs, geography, animals, angels, devils, Witches, charms, the weather, and a host of other subjects ·Gain immediate reference to a vast amount of arcane, but completely annotated, magical material ·Find corrected drawings of seals, sigils, and magic squares, and correctly represented geomantic figures ·Explore the practical Kabbalah, geomancy, the magic squares, the elements, the humors, and the Soul of the World ·Consult the new Biographical dictionary for background on each of the hundreds of writers and historical figures referred to by Agrippa ·Consult the new Geographical Dictionary for data on referenced rivers, mountains, nations, citiesmany of which now carry different names. The Three Books of Occult Philosophy is the most complete repository of pagan and Neoplatonic magic ever compiled. This book is packed with material you will not find elsewhere, including copious extracts on magic from obscure or lost works by Pythagoras, Ptolemy, Plato, Aristotle, and many others. Tyson's detailed annotations clarify difficult references and provide origins of quotations, even expanding upon them in many cases, in order to make Agrippa's work more accessible to the modern reader. The Three Books of Occult Philosophy is the ultimate "how-to" for magical workings. It describes how to work all manner of divinations and natural and ceremonial magic in such clear and useful detail that it is stillthe guide for modern techniques. The extensive new supplementary material makes this wisdom practical for use today. The Three Books of Occult Philosophy is an essential reference tool for all students of the occult. Get your copy today. (shrink)

A. W. Brian Simpson, Cannibalism and the Common Law Chicago: The University of Chicago Press, 1984.

. Selective incapacitation reexamined: The national academy of sciences' report on criminal careers and “career criminals”. Criminal Justice Ethics: Vol. 7, No. 1, pp. 19-35.

For statesmen, friendship is the lingua franca of politics. Considering the connections between personal and political friendship, John von Heyking’s The Form of Politics interprets the texts of Plato and Aristotle and emphasizes the role that friendship has in enduring philosophical and contemporary political contexts. Beginning with a discussion on virtue-friendship, described by Aristotle and Plato as an agreement on what qualifies as the pursuit of good, The Form of Politics demonstrates that virtue and political friendship form a paradoxical relationship (...) in which political friendships need to be nourished by virtue-friendships that transcend the moral and intellectual horizons of the political society. Von Heyking then examines Aristotle’s ethical and political writings – which are set within the boundaries of political life – and Plato’s dialogues on friendship in Lysis and the Laws, which characterize political friendship as festivity. Ultimately, arguing that friendship is the high point of a virtuous political life, von Heyking presents a fresh interpretation of Aristotle and Plato’s political thought, and a new take on the most essential goals in politics. Inviting reassessment of the relationship between friendship and politics by returning to the origins of Western philosophy, The Form of Politics is a lucid work on the foundations of political cooperation. (shrink)

Preface LUDWIG von Mises published many books and articles in his long and productive life, each of them making important contributions to the theory and ...

Moral behaviour, based on social norms, is commonly regarded as a hallmark of humans. Hitherto, humans are perceived to be the only species possessing social norms and to engage in moral behaviour. There is anecdotal evidence suggesting their presence in chimpanzees, but systematic studies are lacking. Here, we examine the evolution of human social norms and their underlying psychological mechanisms. For this, we distinguish between conventions, cultural social norms and universal social norms. We aim at exploring whether chimpanzees possess evolutionary (...) precursors of universal social norms seen in humans. Chimpanzees exhibit important preconditions for their presence and enforcement: tolerant societies, well-developed social-cognitive skills and empathetic competence. Here, we develop a theoretical framework for recognizing different functional levels of social norms and distinguish them from mere statistical behavioural regularities. Quasi social norms are found where animals behave functionally moral without having moral emotions. In proto social norms, moral emotions might be present but cannot be collectivized due to the absence of a uniquely human psychological trait, i.e. shared intentionality. Human social norms, whether they are universal or cultural, involve moral emotions and are collectivized. We will discuss behaviours in chimpanzees that represent potential evolutionary precursors of human universal social norms, with special focus on social interactions involving infants. We argue that chimpanzee infants occupy a special status within their communities and propose that tolerance towards them might represent a proto social norm. Finally, we discuss possible ways to test this theoretical framework. (shrink)

The reinterpretation of Nature by biology, which will prevail in spite of all obstacles, has brought our thinking closer to antiquity, giving us the chance to reinvigorate our perused terminology with the help of the resources to be found in the thoughts of the greatest minds of mankind. The way to Plato thus being cleared, I perceived the idea to seek enlightenment on pressing biological questions from the great Sage. As means to this end, I chose to make Socrates continue (...) one of his dialogues, with the adjustment of giving him the knowledge of our contemporary biological problems. Thus some kind of interaction between the Ancients and ourselves is created, to our considerable benefit. (shrink)

Kritische Grundlegung des transcendentalen Realismus ist ein unveränderter, hochwertiger Nachdruck der Originalausgabe aus dem Jahr 1889. Hansebooks ist Herausgeber von Literatur zu unterschiedlichen Themengebieten wie Forschung und Wissenschaft, Reisen und Expeditionen, Kochen und Ernährung, Medizin und weiteren Genres. Der Schwerpunkt des Verlages liegt auf dem Erhalt historischer Literatur. Viele Werke historischer Schriftsteller und Wissenschaftler sind heute nur noch als Antiquitäten erhältlich. Hansebooks verlegt diese Bücher neu und trägt damit zum Erhalt selten gewordener Literatur und historischem Wissen auch für die Zukunft (...) bei. (shrink)

The Art of Power offers up a challenge to traditional political theory. Diego A. von Vacano provides original interpretations of Machiavelli's oeuvre and of Nietzsche's relationship to politics.

Early on Dietrich von Hildebrand distinguished himself as a thinker with an unusual understanding of human love. His books in the 1920s on man and woman broke new ground and stirred up fruitful controversy. Toward the end of his life he wrote a foundational book on love, The Nature of Love. He had in fact been preparing all his life to write this work; he was so drawn to the philosophical analysis of love that his students long ago had dubbed (...) him doctor amoris, the doctor of love. The Nature of Love is a masterpiece of phenomenological investigation. Not since Max Schelers work on love have the resources of phenomenology been so fruitfully employed for the understanding of what love is and what it is not. (shrink)

ZusammenfassungIm Gegensatz zu Beck und Allison, die dem Gefühl der Achtung eine mehr psychologische oder pädagogische Rolle zuschreiben, wird zu zeigen versucht, dass dieses ebenfalls eine wichtige systematische Funktion zu erfüllen hat: als Triebfeder artikuliert es den heiklen Übergang von der noumenalen zu den phänomenalen Sphäre. In dieser Weise wird erst erklärt, wie es überhaupt möglich ist, dass das Sittengesetz einen Einfluss auf menschliche Handlungen haben kann. Kants System wird dabei im strengen Sinne als Dualismus betrachtete – ein charakteristischer Zug, (...) der nicht durch Interpretationen der Art wie die Zwei‐Aspekten‐Lehre verwischt werden sollte. (shrink)

This article contains an overview of the author's long‐standing involvement with deontic logic, both from a technical and from a wider philosophical point of view. As far as the formal aspects of deontic logic are concerned, the author describes his intellectual development from the original discovery of the analogy between modal (and deontic) notions on the one hand, and quantifiers on the other, through the formulation of a systematic theory of dyadic deontic concepts, to the proposal of a formal logic (...) of action as a foundation for deontic logic. In a more philosophical vein, the author discusses such questions as the very possibility of deontic logic if norms have no truth‐value, the relation between the descriptive interpretation of classical deontic logic and the logic of norm‐propositions, the correct representation of conditional or hypothetical norms, the distinction between moral obligation and practical necessity, and the interdefinability of permission and obligation. (shrink)

Open science will make science more efficient, reliable, and responsive to societal challenges. The European Commission has sought to advance open science policy from its inception in a holistic and integrated way, covering all aspects of the research cycle from scientific discovery and review to sharing knowledge, publishing, and outreach. We present the steps taken with a forward-looking perspective on the challenges laying ahead, in particular the necessary change of the rewards and incentives system for researchers (for which various actors (...) are co-responsible and which goes beyond the mandate of the European Commission). Finally, we discuss the role of artificial intelligence (AI) within an open science perspective. (shrink)

This paper proposes a social account for the origin of the truth value and the emergence of the first declarative sentence. Such a proposal is based on two assumptions. The first is known as the social intelligence hypothesis: that the cognitive evolution of humans is first and foremost an adaptation to social demands. The second is the function-first approach to explaining the evolution of traits: before a prototype of a new trait develops and the adaptation process begins, something already existing (...) is used for a new purpose. Applied to the emergence of declarative sentences (statements), this suggests something already existing––natural signs (such as indexical objects)––was used for the declarative function and thereby integrated into communication. I show that index display (such as the display of hunting trophies) can imply a conceptual structure similar to that informing the syntax of sentences. The view developed in this paper is broadly consistent with the argumentative theory of Mercier and Sperber, which suggests that reasoning is less adapted to decision making than to social purposes such as winning disputes. In this paper I extend this view to the evaluation of propositions expressed in declarative sentences. According to my proposal, the first declarative sentence emerged as the negation of the (implicit) negation of an implicit statement. Thereby, I suggest that the binary structure of the truth value underlying any declarative sentence is founded on disagreements based on conflicts of interests. (shrink)

The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.

Zwei Körper, die exakte Spiegelbilder voneinander sind, nennt Kant „inkongruente Gegenstücke”. Als Beispiel für solche Figuren, die strecken- und winkelgleich, aber nicht kongruent sind, mithin durch Translation und Drehung nicht zur Deckung gebracht werden können, gelten die rechte und die linke Hand eines Menschen. Obwohl diese beiden Objekte in den Relationen ihrer Teile und in der Größe ihrer Ausdehnung völlig gleich sind, sind sie dennoch nicht bloß hinsichtlich Ort und Lage verschieden. Beruht ihre Verschiedenheit auf einem inneren Grund oder auf (...) einem äußeren? Machen verschiedene intrinsische oder verschiedene extrinsische Eigenschaften sie verschieden? Nach der relationalen Raumauffassung, wie sie Leibniz vertritt, müßte die Verschiedenheit inkongruenter Objekte auf verschiedenen extrinsischen Eigenschaften beruhen. Im Gegensatz dazu vertritt Kant die Auffassung, der Unterschied solcher Objekte habe einen inneren Grund. Damit spreche das Phänomen inkongruenter Gegenstücke gegen die Leibnizsche Raumkonzeption. Andererseits aber sprechen gewichtige Gründe gegen die absolute Raumauffassung Newtons. Es bedürfe folglich, so Kant, einer neuartigen Konzeption des Raumes. Als eine solche kann die in der Kritik der reinen Vernunft entwickelte Auffassung gelten, die sich von den beiden vorgefundenen darin unterscheidet, daß der Raum ursprünglich subjektiv statt ursprünglich objektiv ist. (shrink)

Purpose: The paper contributes to the naturalization of epistemology. It suggests tentative itineraries for the progression from elementary experiential situations to the abstraction of the concepts of unit, plurality, number, point, line, and plane. It also provides a discussion of the question of certainty in logical deduction and arithmetic. Approach: Whitehead's description of three processes involved in criticizing mathematical thinking (1956) is used to show discrepancies between a traditional epistemological stance and the constructivist approach to knowing and communication. Practical implications: (...) Reducing basic abstract terms to experiential situations should make them easier to conceive for students. (shrink)

Gentzen's “Untersuchungen” [1] gave a translation from natural deduction to sequent calculus with the property that normal derivations may translate into derivations with cuts. Prawitz in [8] gave a translation that instead produced cut-free derivations. It is shown that by writing all elimination rules in the manner of disjunction elimination, with an arbitrary consequence, an isomorphic translation between normal derivations and cut-free derivations is achieved. The standard elimination rules do not permit a full normal form, which explains the cuts in (...) Gentzen's translation. Likewise, it is shown that Prawitz' translation contains an implicit process of cut elimination. (shrink)

The article examines the record of compliance with the UN Committee against Torture’s decisions in individual complaints cases. Theoretically, I expect that compliance will be the outcome of a combination of normative and rationalist factors: States committed to human rights protection will comply even in the absence of enforcement but only as long as compliance costs remain relatively low. Using a data set covering all adverse decisions issued until 2018 and information on their compliance status, I employ fuzzy-set qualitative comparative (...) analysis to identify necessary and sufficient conditions for the outcomes of compliance and noncompliance. The analysis reveals that the conditions tested—liberal democracy, nonuse of political terror, violation type, and strong civil society—are in part individually (near-)necessary and jointly sufficient for compliance, while the presence of their complements is consistent with noncompliance. The Committee against Torture thus appears to be able to elicit (some) state compliance with its decisions, if mostly only with respect to certain kinds of states and select types of violations. (shrink)