This is a German translation with commentary of Aristotle’s Prior Analytics, Book I. The introduction (‚Einleitung‘, pp. 97–182) contains a concise history of the reception of Aristotle’s syllogistic from Theophrastus to Kant and Hegel. The commentary places special attention to the modal chapters (i. e. I 3 and 8–22). Aristotle’s modal syllogistic is treated with more sympathy than in other modern commentaries and discussions of this part of Aristotle’s logic.

Aristotle asserts in Met. Theta 4 that „if A, then B“ is a consequence of „if A is possible, then B is possible,“ for any sentences A and B. His assertion has often been questioned, or even been suspected to be a crude mistake. After a discussion of a typical objection, it is shown that a plausible reading of Aristotle’s claim is true: The twice occurring „if – then“ has to be understood in the sense of logical entailment, and sentences (...) suitable as substitutes for the variables „A“ and „B“ are required to contain no modal expressions. The claim in question is the converse of the assertion also advanced in Theta 4 that „if A is possible, then B is also possible“ is a consequence of „if A, then B.“ An application of this cognate of pertaining to the incommensurability of a square’s diagonal is expounded. In the final section, the argument advanced by Aristotle himself in defence of is evaluated. (shrink)

The core ideas of the dialogicalapproach to modal propositional logic are explainedby means of an elementary example. Subsequently,ways of extending this approach to the system G ofso-called provability logic are checked, therebyraising the question whether the dialogician is inneed of shaping his Nichtverzögerungsregel(non-delay-rule), in order to get it sufficiently precise,in different ways for different modal systems.

This article investigates the prospect of giving de dicto- and de re-necessity a uniform treatment. The historical starting point is a puzzle raised by Aristotle's claim, advanced in one of the modal chapters of his Prior Analytics, that universally privative apodeictic premises simply convert. As regards the Prior and the Posterior Analytics, the data suggest a representation of propositions of the type in question by doubly modally qualified formulae of modal predicate logic that display a necessity operator in two distinct (...) positions. Can the N-operator occurring in these positions be given a unified semantical treatment (which would justify dispensing with a notational differentiation)? A positive answer, based on a suitably shaped truth condition for N-formulae, is given, and is supported in the final section with an alternative proof theoretically based conception of a property's essential belonging to an individual. (shrink)

An outstanding philosopher-logician, Gottlob Frege's work has received much attention in recent years. In the pursuit of Frege's main goal to solidify the foundations of mathematics and scientific work, Frege conceived a comprehensive philosophy of language and developed the main thesis of logicism, that mathematics is reducible to logic. This book contains essays covering a large range of issues related to Frege that will be of great interest to philosophers working on these issues. This volume represents an important addition to (...) the study of Frege. This book contains essays from some of the most important contemporary philosophers investigating Frege's ideas. Treating issues of contemporary interest, this book discusses topics either in a Fregean spirit or in dialogue with Frege's original views. The wide implications of Frege's views are evident in the variety of topics presented in this volume, from the Frege fundamentals to innovative interpretations that break new ground in the study of Frege. Key papers concern the ontological status of propositions and concepts, recent attempts to improve on the semantics of singular terms, the question of how to construe the content of concept-expressions, and other themes within the common grounds in which ontology and philosophical semantics intersect. (shrink)

Deontic logicians try to fix the logically relevant aspects of the meanings of normative expressions and to reveal the logical relations between the corresponding sentences. From the very beginning, however, logicians and philosophers engaged in work on axiomatic Systems of deontic logic have faced so called problem of the "paradoxes of deontic logic". What is covered by this label are deontic formulae which are provable in logic harmless-looking axiomatic systems, but which seem to be clearly false on certain natural interpretations (...) providing them with that content. The problem of these paradoxes has been intensively discussed within the last decades. In the course of the debate, even quite fundamental assumptions of deontic logic have been newly questioned - for it seemed possible that involvement in paradoxes flows already from these very assumptions. In this work a new kind of formal semantics for a deontic language is developed. It embodies semantical considerations inspired by R.M. Hare's analyses of the meanings of normative expressions, a point of special importance being the representation within semantics of Hare's central concept of the universalizability of normative propositions. Those deontic formulae typically suspected of paradoxicality are shown by the author to be non-theorems of the logic thereby generated. Some of the customary formal semantics for deontic logic prove to be special cases of the semantics put forward, so that the author is in a position to explain the coming about of several typically paradoxical formulae: they become formal semantically valid just in case certain restrictions are introduced into the new semantic framework established. The book ends with the result that the assumptions hitherto taken as basic for deontic logic may be retained, at least as far as the paradoxes are concerned. For it has been shown that one can avoid the paradoxes without dropping those assumptions by use of a more intricate kind of formal semantics. The book will serve as an introduction to central questions of deontic logic, which, unsettled as they were, led to a rather sceptic attitude towards the prospects of this discipline. Nortmann offers a new semantics to overcome the problems. (shrink)

Concepts from the philosophy of science such as the concepts of theoreticity and empirical content have been initially applied primarily in the field of scientific theories. In the following paper, while focussing on several exemplary cases, I shall investigate whether or not such categories can also be meaningfully applied to philosophical theories. Plato's metaphysics of forms stands in the foreground, and, for this philosophical theory, such an application appears to be meaningful. Having established this, we may further explore the question (...) of the relative empirical content of Platonism as compared, say, with Aristotle's property-essentialism. The result of such an investigation is the following. Beginning with a supply of essences of properties, one can create a superstructure which would satisfy the central requirements of the metaphysics of forms ; to such an extent, Platonism, as compared to Aristotelianism, shows no surplus in content , or, to put it another way, Aristotle was not so far from Platonism as he himself believed. (shrink)

The core ideas of the dialogicalapproach to modal propositional logic are explainedby means of an elementary example. Subsequently,ways of extending this approach to the system G ofso-called provability logic are checked, therebyraising the question whether the dialogician is inneed of shaping his Nichtverzögerungsregel(non-delay-rule), in order to get it sufficiently precise,in different ways for different modal systems.

Summary: "Ein Bild sagt mehr als tausend Worte?" Worin gründet diese besondere "Sagkraft" der Bilder, wie sind epistemische Gehalte von Bildern denkbar, die sich einer sprachlichen Vermittlung entziehen, ja: ein genuin bildliches, nicht-sprachliches Erkenntnispotential für sich einfordern?

It is argued that Plato views forms as the proper objects of mathematical research, in contrast to what Aristotle says about the ontologically intermediate state of math?matiká in Platonism. Plato’s particularistic conception of ideas is compared with the nowadays customary mathematical practice of studying types of structures by examining canonical representatives. The case is illustrated by considering the shift from a universalistic conception of natural numbers, in the Frege-Russell-tradition, to a particularistic conception, as in von Neumann. Finally, the characterization of (...) dialectical thinking ventured by Plato at the end of Politeia VI is related, by evaluating Gödel’s incompleteness result, to the Gödelian model of what can be recognized as a partial transcending of the limits of axiomatic systems. (shrink)

In his treatise on sophisms, the medieval logician and philosopher J. Buridan expounded a theory on what we have come to call semantic paradoxes. His theory has not yet been fully understood. The present paper aims at showing that Barwise's and Etchemendy's considerations on paradoxes (founded upon Aczel's non-well-founded sets) provide the framework for an improved understanding. Barwise's and Etchemendy's account is contrasted with Kripke's. Finally, a recent analysis of Buridan's position by Epstein is criticized.

Essentialism is, on the one hand, anchored with considerable firmness in a common sense picture of the world. On the other hand, it was dismissed for logico-philosophical reasons by a scientifically minded theorist like Quine. ``New essentialists'' like Kripke did engage in very profitable theorizing on an essentialist basis, but made no significant effort to investigate the prospects of imparting to an essentialist metaphysics a solid foundation within a scientific world view. These foundational prospects are the concern of the article. (...) – The investigation is guided by two ideas which are elaborated within a proof theoretical framework in the course of the article. First, being an essential F (where ``F'' represents a predicate) is linked with a lifelong possession of the property signified by ``F'' (but there is something more in it). Second, a special kind of necessity is involved in (true) predications of essential F-ness; it should be capable, like possibly all kinds of necessity, of being spelt out, in the final analysis, in terms of the provability of appropriate propositions in appropriate theoretical systems. In outlining the relevant axiomatic bases, the article draws on an early paper by E. Hirsch on individuation and essence. (shrink)

Aristotle asserts in Met. Theta 4 that „if A, then B“ is a consequence of „if A is possible, then B is possible,“ for any sentences A and B. His assertion has often been questioned, or even been suspected to be a crude mistake. After a discussion of a typical objection, it is shown that a plausible reading of Aristotle’s claim is true: The twice occurring „if – then“ has to be understood in the sense of logical entailment, and sentences (...) suitable as substitutes for the variables „A“ and „B“ are required to contain no modal expressions. The claim in question is the converse of the assertion also advanced in Theta 4 that „if A is possible, then B is also possible“ is a consequence of „if A, then B.“ An application of this cognate of pertaining to the incommensurability of a square’s diagonal is expounded. In the final section, the argument advanced by Aristotle himself in defence of is evaluated. (shrink)