Kohlenbach, U., Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation, Annals of Pure and Applied Logic 64 27–94.We consider uniqueness theorems in classical analysis having the form u ε U, v1, v2 ε Vu = 0 = G→v 1 = v2), where U, V are complete separable metric spaces, Vu is compact in V and G:U x V → is a constructive function.If is proved by arithmetical means from analytical assumptions x (...) εXy ε Yx z ε Z = 0) only , then we can extract from the proof of → an effective modulus of uniqueness, which depends on u, k but not on v1,v2, i.e., u ε U, v1, v2 ε Vu, k εG, G 2-φuk→dv2-itk). Such a modulus φ can e.g. be used to give a finite algorithm which computes the zero of G on Vu with prescribed precision if it exists classically.The extraction of φ uses a proof-theoretic combination of functional interpretation and pointwise majorization. If the proof of → uses only simple instances of induction, then φ is a simple mathematical operation. (shrink)

Ein Gespenst geht um in den Wissenschaften - das Gespenst des Gedankenexperiments. Gedankenexperimente verheißen Erkenntnisgewinn ohne empirische Arbeit - was vor dem Selbstverständnis der modernen Naturwissenschaften jedoch einer Unmöglichkeit gleichkommt. Und doch zieht sich das Forschen mit Gedankenexperimenten wie ein roter Faden durch die lange Tradition in den empirischen Wissenschaften von ihren Anfängen bei Stevin, Galilei und Newton bis heute.

The concept of genetic information is controversial because it attributes semantic properties to what seem to be ordinary biochemical entities. I argue that nucleic acids contain information in a semantic sense, but only about a limited range of effects. In contrast to other recent proposals, however, I analyze genetic information not in terms of a naturalized account of biological functions, but instead in terms of the way in which molecules determine their products during processes known as template-directed syntheses. I argue (...) that determining an outcome in a certain way is constitutive for being an instruction. On this account, the content of genetic information is identified with the template's properties, which determine the product in the way constitutive for instructions. (shrink)

The genetic code has been regarded as arbitrary in the sense that the codon-amino acid assignments could be different than they actually are. This general idea has been spelled out differently by previous, often rather implicit accounts of arbitrariness. They have drawn on the frozen accident theory, on evolutionary contingency, on alternative causal pathways, and on the absence of direct stereochemical interactions between codons and amino acids. It has also been suggested that the arbitrariness of the genetic code justifies attributing (...) semantic information to macromolecules, notably to DNA. I argue that these accounts of arbitrariness are unsatisfactory. I propose that the code is arbitrary in the sense of Jacques Monod's concept of chemical arbitrariness: the genetic code is arbitrary in that any codon requires certain chemical and structural properties to specify a particular amino acid, but these properties are not required in virtue of a principle of chemistry. This notion of arbitrariness is compatible with several recent hypotheses about code evolution. I maintain that the code's chemical arbitrariness is neither sufficient nor necessary for attributing semantic information to nucleic acids. (shrink)

For the first time in his Doctrine of Right, Kant employs an expanded, three dimensional concept of public law. In addition to constitutional law, it also includes international law and cosmopolitan law. Each of these concepts of law is assigned its own principle of reason: constitutional law declares that a republic is the only rightful constitution for an individual state; international law requires at least an association of states with higher level instruments of coercion; and cosmopolitan law primarily defines the (...) basic rights of stateless peoples or individuals with respect to existing states. For the principles of reason for constitutional and international law, Kant formulates permissive laws, which allow for imperfections in an effort to promote the optima which the legal principles of reason dictate. Kant justifies these less perfect solutions not only with pragmatic considerations but also with reasons relating to the theory of the sovereignty of nations. Kants Rechtslehre verwendet erstmals einen erweiterten, dreidimensionalen Begriff des öffentlichen Rechts, der neben dem Staatsrecht nun auch das Völkerrecht und das Weltbürgerrecht umfaßt. Jeder dieser Begriffssphären wird ein eigenes vernunftrechtliches Prinzip zugeordnet: das Staatsrecht erklärt die Republik zur einzig rechtmäßigen Verfassung, während das Völkerrecht mindestens eine Staatenassoziation mit höherstufiger Zwangsgewalt erfordert und das Weltbürgerrecht in der Hauptsache die elementaren Rechte von staatslosen Völkern oder Einzelpersonen gegenüber Staaten definiert. Für das staatsrechtliche und das völkerrechtliche Prinzip formuliert Kant Erlaubnisgesetze, die zur Beförderung der vernunftrechtlichen Optima Minderformen zulassen, zu deren Rechtfertigung Kant nicht allein pragmatische, sondern ebenso volkssouveränitätstheoretische Gründe anführt. (shrink)

A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel'sT as well as Kleene/Feferman's ) is applied to systems of intuitionistic and classical arithmetic (H andH c) in all finite types with full induction as well as to the corresponding systems with restricted inductionĤ↾ andĤ↾c.H and Ĥ↾ are closed under a generalized (...) fan-rule. For a restricted class of formulae this also holds forH c andĤ↾c.We give a new and very perspicuous proof that for each one can construct a functional such that $\tilde \Phi \alpha $ is a modulus of uniform continuity for Φ on {β1∣∧n(βn≦αn)}. Such a modulus can also be obtained by majorizing any modulus of pointwise continuity for Φ.The type structure ℳ of all pointwise majorizable set-theoretical functionals of finite type is used to give a short proof that quantifier-free “choice” with uniqueness (AC!)1,0-qf. is not provable within classical arithmetic in all finite types plus comprehension [given by the schema (C)ϱ:∨y 0ϱ∧x ϱ(yx=0⇔A(x)) for arbitraryA], dependent ω-choice and bounded choice. Furthermore ℳ separates several μ-operators. (shrink)

It is well known by now that large parts of mathematical reasoning can be carried out in systems which are conservative over primitive recursive arithmetic PRA . On the other hand there are principles S of elementary analysis which are known to be equivalent to arithmetical comprehension and therefore go far beyond the strength of PRA . In this paper we determine precisely the arithmetical and computational strength of weaker function parameter-free schematic versions S− of S, thereby exhibiting different levels (...) of strength between these principles as well as a sharp borderline between fragments of analysis which are still conservative over PRA and extensions which just go beyond the strength of PRA. (shrink)

1. T. Darstellung -- 2. T. Anmerkungen und Register.

An original analysis of the parallels between the arrested moment in photography and in the traumatized psyche.

The paper presents a refined method of extracting reasonable and sometimes unexpected programs from classical proofs of formulas of the form ∀x∃yB . We also generalize previously known results, since B no longer needs to be quantifier-free, but only has to belong to a strictly larger class of so-called “goal formulas”. Furthermore we allow unproven lemmas D in the proof of ∀x∃yB , where D is a so-called “definite” formula.

I understand the claim that there is a right to work as the claim that involuntary unemployment is an injustice that requires of justice enforcement institutions to stop it. I argue that in present conditions of high productivity it is more consistent with the liberal tradition to proclaim a right to develop one’s capabilities than a right to work. The steps of my argument are: (1) An important though not the only reason for considering unemployment unjust has been what I (...) call the Promethean idea of society. (2) The Promethean idea is implied by the liberal idea of rights. (3) There are two conceptions of the Promethean idea, the centralist and the autonomous one. (4) Only the latter is acceptable. (5) Involuntary unemployment is unjust even if the dole is decently high. (6) The injustice of unemployment can be stopped only by institutions that enable everyone to use their capabilities in realizing the Promethean idea. (7) One such institution is basic income. (8) As employment is not necessary for survival, we should replace the right to work with a right to develop one’s capabilities. (shrink)

With the rigorous development of modal logic in the first half of the twentieth century, it became custom amongst philosophers to characterize different views about necessity and possibility in terms of rival axiomatic systems for the modal operators ‘ ’ (‘possibly’) and ‘ ’ (‘necessarily’). From the late 1950s onwards, Arthur Prior began to argue that temporal distinctions ought to be given a similar treatment, in terms of axiomatic systems for sentential tense operators, such as ‘P’ (‘it was the case (...) that’) and ‘F’ (‘it will be the case that’).1 My aim here is to give a brief survey of the extent to which time can be treated on the model of modality. I shall not try to address the further question of whether such ‘modal’ accounts of time are to be preferred over ‘spatial’ accounts that treat times more like places. (shrink)

Biographical note: Thomas Alkemeyer (Dr. phil.) ist Professor für Soziologie und Sportsoziologie an der Carl von Ossietzky Universität Oldenburg. Ulrich Bröckling (Dr. phil.) ist Professor für Kultursoziologie an der Albert-Ludwigs-Universität Freiburg. Tobias Peter (Dr. rer. pol.) ist wissenschaftlicher Mitarbeiter am Institut für Soziologie der Albert-Ludwigs-Universität Freiburg.

The aim of this paper is to explain the Kantian concept of philosophy according to which philosophy can be understood as the narrow door to the teaching of wisdom. This discussion is guided by the question about the relation between logos and mythos. The thesis is that the awareness of the limits of logos, the scientific approach to the world, can be regarded as a presupposition for a proper understanding of mythos, the articulation of wisdom, which expresses the unity of (...) contradictory elements of life. Philosophy has the function of mediating between reason and wisdom by making explicit the limits of scientific explanation. This opens a field of unrestricted and therefore not scientifically explicable thoughts: the sphere of ideas that are accessible in Ethics and Aesthetics. (shrink)

Exploration of the process/es and features of theorizing. Investigation of the so-called methods, techniques and tools of doing philosophy or philosophizing and illustrating that they resemble the methods of the process/es of theorizing. Showing that the some or most of the same process are implicit and underlying social theory and the development of such theory with Habermas as example.

Praxeology as theoretical concept has obtained growing attention in recent years, at the same time there is a lack of empirical findings upon its scope in applied research. The contributions of this volume prove the operational feasibility and heuristic capacity of the praxeological approach in an interdisciplinary perspective and based on specific research questions.".