First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). The central question here is that about the actual reason for antinomic structures. It turns out to be a form (...) of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). ---------- Zunächst wird gezeigt, dass das Verbot sprachlicher Selbstreferenz als Lösung des Antinomienproblems einen pragmatischen Widerspruch enthält und damit nicht nur zu restriktiv, sondern geradezu inkonsistent ist (Kap.1). Ferner werden Möglichkeiten nicht-restriktiver Strategien zur Antinomienvermeidung diskutiert, wobei sich die explizite Einbindung der – pragmatisch präsupponierten – Konsistenzforderung als optimale Strategie erweist (Kap.2). Zentral ist hier die Frage nach dem eigentlichen Grund antinomischer Strukturen. Er erweist sich als eine Form von negativer Selbst-Bedingung (Kap.3). Dies nötigt zu einer Klärung des Status negativer Begriffe (Kap.4). Die Verallgemeinerung dieser Überlegungen (Kap.5) leitet über zur eigentlichen Analyse der antinomischen Grundstruktur (Kap.6): Entscheidend zur Pragmatik des Begriffs gehört, dass ihm eine Bedeutung positiv zukommt, sodass durch den Begriff qua Begriff stets auch Positivität konstituiert ist. Dadurch ist ein negativer Begriff durch eine prinzipielle Ambivalenz gekennzeichnet: In semantischer Hinsicht hat er negativen Charakter, in seinem pragmatischen Status als Begriff hingegen positiven Charakter. Ist die Bedeutung insbesondere die eines negativen Selbstbezugs, führt die Ambivalenz zur antinomischen Konstellation einer negativen Selbst-Bedingung – das ist hier der springende Punkt! Der Begriff besitzt so die durch ihn definierte Eigenschaft genau dann, wenn er sie nicht besitzt und umgekehrt. Die nähere Analyse zeigt, dass hierbei die Funktion reflexiver Strukturen für das Auftreten von Antinomien weitaus differenzierter zu beurteilen ist, als bisherige Auffassungen nahelegen. Nicht nur dass in diesem Kontext vier Formen von Reflexivität – ontische, semantische, pragmatische Reflexivität und insbesondere auch die Form negativer Selbstbedingung – unterschieden werden müssen; es zeigt sich auch, dass diese in schwer durchschaubarer Weise ineinander verschränkt sind. Die damit verbundene erstaunliche Beziehungsvielfalt läßt die Irritation, die seit je vom Antinomienproblem ausging, begreiflicher erscheinen. In der entwickelten pragmatischen Perspektive werden ferner Parallelen zur Struktur von Selbstbewußtsein sichtbar (Kap.7). Ich schließe mit Überlegungen zur Bedeutung der antinomischen Struktur für das Problem der Dialektik, insbesondere zur Synthesebildung einander ausschließender Bestimmungen (Kap.8). (shrink)

From a historical perspective the reflection of opposites is a creative strategy of coping with infinite regress. The lawfulness of law is only a particular version of the general paradox that occurs when a distinction is applied to itself. Common legal techniques of avoiding the paradox of self-reference amount to evacuating it or to building hierarchies. Modern strategies futurize the problem under the paradigms of autonomy and procedurality. With increasing complexity legal self-descriptions all the more cling to the ideals of (...) completeness, coherence, and accurate generalisation. However, one can retrace antinomical structures: The legal system is at the same time incomplete, caught in multiple binds, and inadequate from case to case due to highly selective concepts. The law keeps producing conflicts that again must be legally resolved. (shrink)

Perspectives on old age are characterized by an antinomy of veneration and contempt. This paper explores how this antinomy is spelled in philosophical discourses and how it intersects with the antithesis of fool and sage. According to a Platonist or Antiochean account of ontogenesis, an individual’s development is conceived as an approximate instantiation of an ideal form of “man,” which tends to divide old people into successes and failures. In contrast to this, the Stoic theory of oikeiōsis envisages a continuous (...) process of self-constitution and self-integration that allows for continuous progress and a fundamental reorientation at any age. The elderly and ailing Stoic thus exemplifies not resignation but hope, that it is never too late to turn one’s life into a success story. (shrink)

This concise work is a study of the semantical aspects of various paradoxes arising in formal logic. The author constructs a second-order system T with an interpretation in order to provide apparatus for stating and dodging the antinomies. After presenting a number of paradoxes, the author discusses a semantic vicious-circle principle, and provides a clarification of the problems by its application. He then discusses semantic aspects of some classical meta-mathematical results of Gödel, Tarski, Kleene, and Turing on unsolvable problems. Also (...) treated is the topic of impredicative definition in mathematics, especially as it relates to the vicious-circle principle.—P. J. M. (shrink)

La solution des antinomies s’accomplit en 3 étapes. 1° La théorie des types de Russell avec l’axiome de réductibilité. 2° Ramsey divise les antinomies en deux groupes. Le premier groupe reçoit sa solution de la simple théorie des types ; seul, le groupe élargi exige l’axiome de réductibilité. 3° Hilbert fonde la théorie métamathématique de la preuve, que les logiciens polonais élargissent en une métalogique. Gödel découvre l’arithmétisation et il prouve l’existence de propositions insolubles. Tarski montre que le concept de (...) vérité ne peut être défini sans contradiction que dans un métalangage. Carnap généralise ce résultat, ce qui fait que les antinomies syntactiques sont sans dommage pour la science. (shrink)

According to Kant, concepts can be used in three different ways, i.e. an empirical (= pre-philosophical) use, a transcendentally real (= philosophically inadequate) use, and a transcendentally ideal (= philosophically reasonable) use. Regarding the concept of the world as a whole, however, Kant misrepresents the empirical meaning and therefore overlooks the transcendentally ideal understanding of “everything”. Along this guiding line, the paper defends Kant’s program of showing that spatiotemporal objects are conditioned by subjective, non-empirical conditions against the charge that it (...) is inconsistent with Kant’s alleged solution of the antinomies. It turns out that Kant’s program is consistent both with ontological realism about the world and with empirical realism about, e.g., the Big Bang. The remaining problem is how to formalize in modal logic unrestricted quantification in its transcendentally ideal usage. (shrink)

Bernard Bolzano criticised Kant's philosophy so vehemently that his pupil Franz Prihonsky called him "Anti-Kant". One of his criticisms concerns Kant's cosmological antinomies. The context of this critique is the problem of limits of knowledge. Kant wanted to prove that there are such boundaries, and to show where these are located. In this paper we will schematize Kant's antinomies and summarize Bolzano's criticism, which is distributed over his and his student's work. At the beginning we will work out the theoretical (...) differences between Kant's and Bolzano's philosophy to see what roles these play in the construction of the antinomies. (shrink)