Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992

Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs

The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources

Virtual Reality: Consciousness Really Explained! (Third Edition)

Employing the ideas of modern mathematics and biology, seen in the context of Ernst Cassirer's "Symbolic Forms, the author presents an entirely new and novel solution to the classical mind-brain problem. This is a "hard" book, I'm sorry, but it is the problem itself, and not me which has made it so. I say that Dennett, and, indeed, the whole of academia is wrong

Putting Chinese natural knowledge to work in an eighteenth-century Swiss canton: the case of Dr Laurent Garcin

Symposium: S048 - Putting Chinese natural knowledge to work in the long eighteenth centuryThis paper takes as a case study the experience of the eighteenth-century Swiss physician, Laurent Garcin (1683-1752), with Chinese medical and pharmacological knowledge. A Neuchâtel bourgeois of Huguenot origin, who studied in Leiden with Hermann Boerhaave, Garcin spent nine years (1720-1729) in South and Southeast Asia as a surgeon in the service of the Dutch East India Company. Upon his return to Neuchâtel in 1739 he became primus inter pares in the small local community of physician-botanists, introducing them to the artificial sexual system of classification. He practiced medicine, incorporating treatments acquired during his travels. taught botany, collected rare plants for major botanical gardens, and contributed to the Journal Helvetique on a range of topics; he was elected a Fellow of the Royal Society of London, where two of his papers were read in translation and published in the Philosophical Transactions; one of these concerned the mangosteen (Garcinia mangostana), leading Linnaeus to name the genus Garcinia after Garcin. He was likewise consulted as an expert on the East Indies, exotic flora, and medicines, and contributed to important publications on these topics. During his time with the Dutch East India Company Garcin encountered Chinese medical practitioners whose work he evaluated favourably as being on a par with that of the Brahmin physicians, whom he particularly esteemed. Yet Garcin never went to China, basing his entire experience of Chinese medical practice on what he witnessed in the Chinese diaspora in Southeast Asia (the ‘East Indies’). This case demonstrates that there were myriad routes to Europeans developing an understanding of Chinese natural knowledge; the Chinese diaspora also afforded a valuable opportunity for comparisons of its knowledge and practice with other non-European bodies of medical and natural (e.g. pharmacological) knowledge.postprin

Systematische Ganzheitlichkeit : eine methodologische Vermittlung zwischen Perspektivität und Universalität

Zusammenfassung: Diese Untersuchung ist das Ergebnis einer langjährigen Entwicklung, motiviert durch die Erfahrung von Widersprüchen und Zwängen in der internationalen beruflichen Praxis, die eine gründliche Auseinandersetzung mit den Möglichkeiten einer ganzheitlichen Erfassung von Situationen und Zusammenhängen nahe legten. Das Selbstverständnis von Philosophie hat sich dahin gehend entwickelt, Strukturen von Aussagen zu entwerfen und zu debattieren über Dinge und Zustände der Welt. Weil keine der daraus hervorgegangenen Positionen universelle Geltung beanspruchen kann, rivalisiert eine Unzahl von Versuchen, ohne daß eine wirklich ganzheitlich zielführend werden könnte. Im hier vorgelegten Ansatz ist die Grundidee, nicht wie üblich sofort über weltliche Dinge zu urteilen – was prinzipiell zu blinden Flecken und unvollständigen Welt¬bildern führen muß – sondern erst das Instrumentarium des Begrifflichen in seiner Eigendynamik kompromißlos auszuloten, durch welches jede Prädikation erfolgt. Für diese Klärung setzt der hier vorgeschlagene Ansatz beim Gesamtzusammenhang aller potentiellen Begrifflichkeit an, der die streng universell gültigen Ordnungen in der Wirklichkeit zugänglich macht und auch die Basis für die Grundgesetze der Logik bildet. In der hier vorgelegten Darstellung der Zusammenhänge umfaßt das Vorwort die Bezüge zwischen subjektiver Erfahrung und objektiver Problematik (Kapitel 1). Das Anliegen als solches wird in der einführenden Diskussion diskutiert (Kapitel 2). Die Darstellung erfolgt in sieben Stufen bzw. Unterkapiteln: in 2.1 das Thema ergreifend, um die Basis für die Untersuchung zu legen; 2.2 die Probleme untersuchend zwischen rationalem Zugang und ganzheitlicher Erfassung, dadurch die Lösungsidee grob umreißend; 2.3 die Ursache von Behinderung im ganzheitlichen Erfassenwollen aufgreifend: 'Eingreifen statt Einfühlungsvermögen'; 2.4 die durch diese mentale Attitüde real erzeugte Selbstbegrenzungen auslotend; 2.5 die prinzipielle Vermeidbarkeit von solchen Grenzen erörternd, wie auch deren Auflösbarkeit; 2.6 eine naturgegebene inhalslogische Gesetzmäßigkeit aufspürend, welche im Begrifflichen erfüllt sein muß, wenn lückenlose Begreif¬barkeit erreichbar werden soll; 2.7 den Bezug zum Gesamtzusammenhang als Verbund aller Inhalte umreißend. Dieser Denkpfad des reinen 'Horchens' kommt ohne jede Voraus-Setzung aus (es müssen aber bestimmte Vor-Bedingungen erfüllt sein); ihn beschreitend, wird die Qualität des vorgeschlagenen Lösungsansatzes – 'systematische Aufmerksamkeit' – allmählich erkennbar. Die ganzheitliche Auslotung der Eigengesetzlichkeit von perspektivischem Denken läßt eine Universalität erreichbar werden, die – im Gegensatz zu den üblichen philosophischen und wissenschaftlichen Methoden – allgemein die Brücke zwischen Perspektivität und Universalität zu schlagen erlaubt. Das Mittel dafür liegt in den grundbegrifflichen Strukturen, welche aus den rein logischen Implikationen eines Frage-Inhalts heraus entfaltet werden können und dann als kategoriale Ganzheit angewendet werden sollten. Die Methode im Vorgehen ist, den Inhalt einer Fragerichtung ganz auf sich selbst anzuwenden (vollständige Selbstbezüglichkeit – die in traditionellen Ansätzen begrenzt ist, aber in rein inhaltslogischem Vorgehen erreichbar). Es kommen die je entsprechenden rein inhaltlich bestimmten und streng polaren Grundbegrifflichkeiten zum Tragen, und das Ergebnis ist die je relevante Vierheit ('Tetrade') von konjugierten Kategorien. Es sind begriffliche Kontinua, welche heuristisch relevant und auf schlechthin alle Strukturen für die phänomenologische Erfassung anwendbar sind, nunmehr mit einer präzisen Ausrichtung. Deshalb bestehen im vorgeschlagenen Ansatz – als 'systematische Aufmerksamkeit' bezeichnet – keine disziplinären Grenzen; im Gegenteil erlaubt er eine prinzipiell unbegrenzte Inter- und Transdiziplinarität. Um die streng allgemeine Anwendbarkeit dieses Ansatzes nachzuweisen, wird er in Kapitel 3 auf die Geowissenschaften angewandt. Diese Disziplin ist dafür besonders geeignet, weil sie in einem homogenen begrifflichen Instrumentarium die gesamte Spannweite vom Mineralischen über das Vegetabile und Sinnesorientierte bis zum Mentalen und Sozialen klar erfaßbar machen sollte. Just dies ist eine der Stärken des vorgeschlagenen Denkansatzes. Die Problematik wird im Unterkapitel 3.1 angegangen durch eine Erörterung der methodologischen Desiderate, dabei die Mathematik und Thermodynamik erörternd als eine Art von lingua franca zwischen heutigen wissenschaftlichen Disziplinen allgemein. Anschließend werden in Unterkapitel 3.2 die Bereiche in den Geowissenschaften kurz im Lichte der 'systematischen Aufmerksamkeit' beleuchtet: (1) physische Geographie als 'Speicher', 'Regler' und 'Prozeß', (2) Klimakunde / Meteorologie als 'Energie' und 'Information', (3) Bodenkunde als Verbindungsort von Anorganik und Organik, (4) Geoökologie mit den 'homogenen Einheiten' der naturräumlichen Gliederung, (5) Biogeographie mit den Biozönosen, Biotopen, und den Stufen des Organischen, (6) Humangeographie mit der Autonomie und Heteronomie des Menschen in seiner individuellen und sozialen Organisation, (7) theoretische Geowissenschaft als Ort der prinzipiellen Integration aller Seinsebenen. In Unterkapitel 3.3 wird noch kurz die Eigengesetzlichkeit der Einwirkung des Menschen auf die Natur umrissen. Kapitel 4 versammelt kurze Kommentare zu den akkumulierten Publikationen. Nach Glossar und Literatur folgen in einem Quasi-Kapitel 5 die neun akkumulierten Publikationen selbst. Die Untersuchung als Ganze ist durchgehend paginiert. ---------- Summary: In my professional life, partly in international planning and urban design, I experienced massive contradictions in the official line of thought, producing unnecessary conflict. Philosophy has developed a self-concept of devising and debating structures of statements and states of worldly affairs. Since no attempt of this sort can ever achieve a strictly complete grasp and universal validity, myriads of them are rivaling, but ultimately all have some flaw. This complex of problems motivated me to go back to university for meditating on integral ways of thinking. The presented investigation is the end result, now molded into a methodological system. The basic idea in the presented approach is not, as usual, to predicate immediately on worldly objects – which inevitably leads to blind spots and incomplete world-views – but to fathom first of all the instrumentation in the conceptual realm with its inherent self-dynamics that underlies all forms of predication. For achieving this objective, the proposed approach sets out on the characteristics of interconnectedness in all potential conceptuality, which allows the universally valid form of order securely to be approached that constitutes also the matrix for the fundamental laws of logic. In the presented investigation, 'Vorwort' means Preface and covers as chapter 1 the relation between subjective authorship and objective questions as implied by the chosen topic. 'Einleitung' means Introduction and features as chapter 1 the issues that follow objectively from the discussed subject matter, namely integral ways of understanding and being, which determine therefore the approach and the method. This chapter offers also an overview over the structure of the problem and possible remedies, working through it in seven steps: in subchapter (2.1) taking hold of its meaning, its intrinsic content, (2.2) outlining a rational approach to this content, and discovering that problems in integral understanding are not imposed by nature, but man-made, (2.3) revealing how habitual approaches manifest – even in pure brain work – not empathy, but a powerful intervention, by setting out on basic assumptions, fundamental beliefs, (2.4) showing the actual results of such interventions, thereby disclosing the type of initiative that allows the problems to be dissolved, (2.5) actually possible procedures for avoiding on principle the occurrence of such discontinuities, (2.6) finding a law of content logic that determines the conceptual conditions for intelligibility and is at the root of the basic laws of formal logic, thereby warranting the general resolvability of the approached complex of problems, (2.7) outlining the bearings of the proposed approach (dubbed 'systematic attentiveness') in the overall interrelations, which the proposed approach allows to be viewed as an ordered complex. The outlined procedure of pure 'listening' can do without any kind of presupposition (while certain preconditions must be fulfilled) and gradually makes intelligible the integral quality of the proposed approach. Fathoming perspectivity in this way fosters a universality that allows – in contrast to usual procedures in philosophy and science – the gap between the two aspects to be bridged. The means for this conciliation reside in the fundamental conceptual structures that can be unfolded out of the purely logical implications of any given query content and should then be applied as a categorial wholeness. The method in proceeding is to apply the given query content onto itself (complete self-referentiality – which is limited in traditional approaches, but attainable in pure content logic). The fundamental conceptual structures that follow in pure content logic from the chosen or given query content can then take effect, and the end result is the respective fourness ('tetrad') of conjugated categories. These constitute conceptual continua that are relevant on the heuristic level and applicable to all structures in phenomenological observation, now in a precise alignment. Due to this quality, the proposed approach – dubbed 'systematic attentiveness' – has no disciplinary limits; on the contrary it allows an inter- and trans-disciplinarity that is on principle unlimited. For verifying the general applicability of 'systematic attentiveness', this approach is applied in chapter (3) to the geosciences because this discipline should cover the full scope from mineral existence to vegetal, sensory and mental life, up to social organization, including all interactions, in a conceptually homogenous way. Subchapter (3.1) contains some general considerations on the theoretical level, broaching the issue of mathematics as lingua franca in the sciences, as well as problems in interpreting thermodynamics, for indicating in (3.2) the applicability of the proposed approach in pivotal sub-disciplines of the geosciences: physical geography (with its categories of 'accumulator', 'regulator' and 'process'), climate studies ('energy' and 'information'), lithosphere (the locus of interlacing inert and alive structures), geoecology, biogeography, human geography, and purely theoretical geosciences, concluding (3.3) with issues of human action on nature. Chapter (4) consists of brief comments to the accumulated articles that follow as such in the fifth and last part of this study. These nine publications reveal other aspects of applicability. They contain some redundancies due to a need of exposing my critique and approach again and again. Most of the papers are written in English, so for Anglophone readers they are self-explanatory