Proceedings of the NATO Advanced Study Institute on Proof and Computation, held in Marktoberdorf, Germany, July 20 - August 1, 1993.

The seventeenth century marked a critical phase in the emergence of modern science. But we misunderstand this process, if we assume that seventeenth-century modes of natural inquiry were identical to the highly specialised, professionalised and ever proliferating family of modern sciences practised today.

There is evidence from neuropsychological and psychophysical measurements that conscious sensory information is processed in discrete time segments. The segmentation process may be described as neuronal activity at a frequency of 40 Hz. Stimulus-induced neuronal activities of this frequency are found in the middle latency range of the auditory evoked potential . First, we have studied the effects of different general anesthetics on MLAEP and auditory evoked 40-Hz activity. Second, we investigated MLAEP and explicit and implicit memory for information presented (...) during cardiac anesthesia. In the awake patients peak latencies of the MLAEP were in the normal range. An auditory evoked 40-Hz activity was present 20–100 ms poststimulus. Under nonspecific anesthetics MLAEP and the 40-Hz activity were suppressed, and under receptor-specific agents MLAEP and the 40-Hz activity were partly preserved. None of the cardiac patients had conscious explicit recall of the intraoperative events, whereas some patients showed unconscious implicit memory for an intraoperative tape message. The implicit memory could be related to midlatency auditory evoked potentials. No implicit memory was detectable when MLAEP and the primary cortical processing of the auditory stimuli and 40-Hz activity were blocked. Implicit memory could be detected in more than 50% of the cases when MLAEP, a 30-Hz activity, and the primary cortical stimulus processing were preserved. In conclusion, our observations support the view that a high frequency oscillatory mechanisms, recorded as a grouped neuronal activity in the MLAEP, may be part of a basic neuronal program for conscious sensory information processing. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non-empty set is injective in classical ZF, which argument fails to work in CZF. The aim of this paper is to shed some light on (...) the problem whether there are (enough) injective sets in CZF. We show that no two element set is injective unless the law of excluded middle is admitted for negated formulas, and that the axiom of power set is required for proving that “there are strongly enough injective sets”. The latter notion is abstracted from the singleton embedding into the power set, which ensures enough injectives both in every topos and in IZF. We further show that it is consistent with CZF to assume that the only injective sets are the singletons. In particular, assuming the consistency of CZF one cannot prove in CZF that there are enough injective sets. As a complement we revisit the duality between injective and projective sets from the point of view of intuitionistic type theory. (shrink)

Even after yet another grand conjecture has been proved or refuted, any omniscience principle that had trivially settled this question is just as little acceptable as before. The significance of the constructive enterprise is therefore not affected by any gain of knowledge. In particular, there is no need to adapt weak counterexamples to mathematical progress.

Cases of acts of solidarity can be divided into at least two groups. Solidarity in a narrow sense of the term refers to what I label project-related solidarity; it is prevalent in the modern world at least as much as it was found in past worlds. In contrast, the philosophical discussions of "solidarity" refer to the altruism and mutuality typically found in close human relationships. This concept of "solidarity" is theoretically unfruitful and even misleading. I propose to abandon the term (...) "solidarity" in order to regain sight of the individual phenomena. When these are taken into consideration, a return to the community is no longer called for. I rather argue that modern societies are perfectly capable of inspiring feelings of loyalty and civic virtues, though not by resorting to the old sources of "solidarity". Modern forms such as free associations, participation and, not least, the existence of a liberal society itself are sufficient. Public discussions of solidarity are additionally distorted by frequent appeals to a normative sense of the term. The argument put forward in this collectivist context that an obligation of solidarity results from gratefulness to the community is not found to be convincing. Individuals are not obliged to be grateful to a nation in a way that would be normatively binding. (shrink)

In his commentary on Aristotle’s Peri hermeneias,1 Abelard distinguishes the form of an expression2 (oratio) from what it says, that is, its content. The content of an expression is its understanding (intellectus). This distinction is surely the most well-known and central idea in Abelard’s commentary. It provides him with the opportunity to distinguish statements (enuntiationes) from other kinds of expressions without implying a diference in their content, since the ability of a statement to signify something true or false (verum vel (...) falsum)3 cannot be found in its content. More precisely, Abelard distinguishes statements both from complete expressions (orationes perfectae) that are not statements but rather questions, requests, commands, etc. and from incomplete expressions, that is, mere word strings (orationes imperfectae), such as homo albus. These kinds of expressions, according to Abelard, do not differ in the understanding they present but in the way they present it. (shrink)

Klaus Peter Mortensen; The Double Call: on Bildung in a Literary and Reflective Perspective, Journal of Philosophy of Education, Volume 36, Issue 3, 16 December.

It has been argued that environmental decision-making can be improved be introducing citizen panels. The authors argue that citizen panels and other models of citizen participation should only be used as a consulting forum in exceptional cases at the local level, not as a real decision-making procedure. But many problems in the field of environmental policy need nonlocal, at least regional or national, regulation due to the fact that they are of national impor-tance. The authors argue that there are good (...) reasons not to institutionalise national citizen panels. They advocate the view that more reasonable and more competent solutions can be found by introducing forms of direct democracy. (shrink)

The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo—Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the axiom of fullness. Together with exponentiation, refinement is equivalent to fullness. None of the defining properties of an ordering is needed, and only refinement for two—element coverings is used. In particular, the Dedekind reals form a set; whence we have also refined an earlier result by Aczel and (...) Rathjen, who invoked the full form of fullness. To further generalise this, we look at Richman's method to complete an arbitrary metric space without sequences, which he designed to avoid countable choice. The completion of a separable metric space turns out to be a set even if the original space is a proper class; in particular, every complete separable metric space automatically is a set. (shrink)

The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

The meaning of optimality and economy in phylogenetics and evolutionary biology is discussed.It can be shown that the prevailing concepts of optimality and economy are equivocal as they are not based on strict theoretical positions and as they have a variable meaning in different theoretical contexts. The ideas of optimality and economy can be considered to be identical with the expectation of a relatively simple order in a particular field of study. Although there exists no way of inferring one or (...) several methods of solving scientific problems from the presupposed idea of economy and optimality, a lack of motivation for scientific investigations would result if the concepts of economy and optimality in nature were dropped. (shrink)

Die kirchen- und dogmengeschichtliche Forschung hat die Beschäftigung mit der Geschichte der Christen im mittelalterlichen Nahen Osten lange vernachlässigt. Für die Zeit nach 700 reduzierte sich Kirchengeschichte in den meisten einschlägigen Handbüchern weitgehend auf die Darstellung der Entwicklung der abendländischen Kirche. Abgesehen von griechischen, russischen und arabischen Arbeiten, die schon aus sprachlichen Gründen meist wenig Beachtung fanden, beschäftigten sich nur wenige Abhandlungen von Spezialisten, die Kenntnisse der orientalischen Sprachen besaßen, mit der Geschichte der einheimischen Christen des Nahen Ostens nach dem (...) 7. Jahrhundert. Erst seit neuester Zeit sind mehrbändige Darstellungen der Kirchengeschichte greifbar, die auch die Geschichte der östlichen Kirchen in befriedigender Weise miteinbeziehen. Wie der von Pahlitzsch in der Einleitung (S. 13–18) gegebene Überblick über den Forschungsstand zeigt, ist jedoch in den letzten beiden Jahrzehnten auch eine Zunahme der wissenschaftlichen Beschäftigung mit der Kirchengeschichte und der gesellschaftlichen Situation der griechisch-orthodoxen Melkiten in den Kreuzfahrerstaaten zu beobachten. (shrink)

Dem Rezensenten obliegt die traurige Pflicht, das letzte Buch des vor kurzem (am 18. August 2003) verstorbenen Berliner Emeritus für Byzantinistik, Paul Speck, zu besprechen. Wie die große Menge seiner früheren Artikel und Monographien beschäftigt sich auch dieses Buch in z.T. polemischer Auseinandersetzung mit den Positionen anderer Forscher mit den Quellen zur byzantinischen Geschichte des 7.–9. Jahrhunderts, also mit der Zeit der sog. Dunklen Jahrhunderte, vor allem mit der Periode des sog. Bilderstreites. Es handelt sich, wie Speck selbst in der (...) Einleitung darlegt (S. 24), bei der vorliegenden Monographie nicht um eine Biographie Kaiser Leons III. (717–741), sondern um eine Analyse der Berichte über die ersten Regierungsjahre dieses Herrschers in drei wichtigen griechischen und lateinischen Quellentexten, nämlich in der Historia syntomos des Patriarchen Nikephoros I. von Konstantinopel (806–815), in der Chronographia des Theophanes (von Speck zu Recht überwiegend als Werk des Georgios synkellos angesehen) und im römischen liber pontificalis. Letzterer spielt allerdings im hier besprochenen Teil 1 nur im XV. Abschnitt (S. 303) eine Rolle. Grundsätzlich gilt nach Speck, daß fast alles, was in der Historia syntomos des Nikephoros berichtet wird, sich meist sogar in derselben Reihenfolge auch in der Chronographia des „Theophanes“ wiederfindet, daß letztere aber zahlreiche zusätzliche Informationen enthält, so daß die Existenz einer beiden gemeinsame Quelle oder Vorlage sehr wahrscheinlich ist (S. 55–56). Bereits in seinen früheren Arbeiten entwickelte er dazu die Hypothese, zwei Materialsammlungen des Georgios synkellos (das sog. vielleicht noch in Palästina verfaßte erste und das dieses bis 815 fortsetzende, in Konstantinopel zusammengestellte zweite Dossier) hätten sowohl für die Historia syntomos des Patriarchen Nikephoros (1. Dossier) als auch für die Chronographia des „Theophanes“ (2. Dossier), aber auch für die christlich-orientalischen Chroniken (diese sind nach Speck vom 1. Dossier abhängig) die Masse der Informationen geliefert (zusammenfassend S. 19–23, ferner S. 95 und S. 375–376). (shrink)

The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.

Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is continuous. By showing that Dini's theorem is equivalent to Brouwer's fan theorem for detachable bars, we provide Dini's theorem with a classification in the recently established constructive reverse mathematics propagated by Ishihara. As a complement, Dini's theorem is proved to be equivalent to the analogue of the fan theorem, weak König's lemma, in (...) the original classical setting of reverse mathematics started by Friedman and Simpson. (shrink)

This study builds upon the top management literature to predict and test antecedents to firms’ engagement in corruption. Building on a survey of 341 executives in India, we find that if executives have social ties with government officials, their firms are more likely to engage in corruption. Further, these executives are likely to rationalize engaging in corruption as a necessity for being competitive. The results collectively illustrate the role that executives’ social ties and perceptions have in shaping illegal actions of (...) their respective firms. (shrink)

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.

Name der Zeitschrift: Deutsche Zeitschrift für Philosophie Jahrgang: 66 Heft: 1 Seiten: 75-86.

Definition of the problem: A `experimental treatment' is defined as the use of a not yet approved medical treatment or product in a single patient outside the scope of regular clinical trials. Especially in oncology the patient is usually in a desperate situation and does not respond to other treatments. Even if he or she is fully informed about the risks he or she may occasionally make an irrational decision.Discussion of the problem: The moral problems in experimental treatments have to (...) do with the medical and scientific quality of the treatment and the patient-physician relationship. It is argued that there are also moral duties for pharmaceutical manufacturers and health insurrance companies.Conclusion: A regulation of experimental treatment trials is necessary both for physicians and for pharmaceutical manufacturers. (shrink)

It is folklore that if a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root, which of course is uniquely determined. Also in Bishop's constructive mathematics with countable choice, the general setting of the present note, there is a simple method to validate this heuristic principle. The unique solution even becomes a continuous function in the parameters by a mild modification of the uniqueness hypothesis. (...) Moreover, Brouwer's fan theorem for decidable bars turns out to be equivalent to the statement that, for uniformly continuous functions on a compact metric space, the crucial uniform “at most one” condition follows from its non-uniform counterpart. This classification in the spirit of the constructive reverse mathematics, as propagated by Ishihara and others, sharpens an earlier result obtained jointly with Berger and Bridges. (shrink)

Dieses Buch ist ein wirklich dringendes Desiderat für alle, die bisher in der einen oder anderen Weise mit dem berühmten Kontobuch des venezianischen Kaufmannes Giacomo Badoer aus seiner Zeit als socio verschiedener Handelsgesellschaften und als correspondente verschiedener Geschäftsfreunde in der spätbyzantinischen Hauptstadt Konstantinopel zu tun gehabt haben. Seit der Edition dieses frühen Zeugnisses entwickelter doppelter Buchführung durch Umberto Dorini und Tommaso Bertelè im Jahre 1956 und in begrenztem Umfang auch schon früher haben Fachvertreter der unterschiedlichsten Disziplinen, Wirtschaftshistoriker, Numismatiker, Mediterranisten und (...) nicht zuletzt Byzantinisten den einzigartigen Quellenwert des Badoer-Buches entdeckt und für ihre verschiedenen wissenschaftlichen Fragestellungen genutzt, und der Verfasser dieser Rezension zählt es noch heute zu den Glücksumständen seines wissenschaftlichen Lebens, daß er gleich zu Beginn seiner Beschäftigung mit dem späten Byzanz ein Exemplar dieses Kontobuches in der Bibliothek des Leipziger Universitätsinstitutes für Allgemeine Geschichte vorfand und es viele Jahre praktisch konkurrenzlos benutzen konnte. Und in den ungezählten Stunden, die er über den wohl in ebenso einsamer Arbeit entstandenen Aufzeichnungen dieses in einer gemieteten Unterkunft hausenden und mit wechselnden Handelsgehilfen und Haussklavinnen arbeitenden und lebenden Venezianers aus vornehmer Familie mit vererbter Profession verbracht hat, sind ihm im Laufe der Zeit immer neue und wichtige Möglichkeiten der Befragung und Auswertung seiner Konten bekannt und bewußt geworden, nicht nur für die Wirtschafts-, sondern auch für die Sozialgeschichte und nicht zuletzt für die politische Geschichte der Zeit, für die Stadt- und die Reichsgeschichte, für Prosopographie und Alltagsgeschichte, und auch das noch längst nicht alles. (shrink)

How are the various classically equivalent definitions of compactness for metric spaces constructively interrelated? This question is addressed with Bishop-style constructive mathematics as the basic system – that is, the underlying logic is the intuitionistic one enriched with the principle of dependent choices. Besides surveying today's knowledge, the consequences and equivalents of several sequential notions of compactness are investigated. For instance, we establish the perhaps unexpected constructive implication that every sequentially compact separable metric space is totally bounded. As a by-product, (...) the fan theorem for detachable bars of the complete binary fan proves to be necessary for the unit interval possessing the Heine-Borel property for coverings by countably many possibly empty open balls. (shrink)