The most elementary way to think about Mathctrtati ca is as an enhance calculator Ã¢â¬â a calculator that does not only numerical computation but also algebraic computation and graphics. Matltcmatica can function much like a standard calt".1a- tor. you type in a question, you get back an answer. But Mat/tctttadca ga's turthcr I ue an ordinary calculator. You can type in questions that require answers that arc longer than a calculator can handle. For example, Matltcmatictt can giv; you thc numerical (...) value of tr to a hundred decimal places, or the exact result for a numerical calculation as complicated as the result of 3)tI0, (m Fig. 1). (shrink)
Patients suffering from chronic obstructive pulmonary diseases, frequently exhibit expiratory airflow limitation. We propose a mathematical model describing the mechanical behavior of the ventilated respiratory system. This model has to simulate applied positive end-expiratory pressure (PEEP) effects during expiration, a process used by clinicians to improve airflow. The proposed model consists of a nonlinear two-compartment system. One of the compartments represents the collapsible airways and mimics its dynamic compression, the (...) other represents the lung and chest wall compartment. For all clinical conditions tested (n=16), the mathematical model simulates the removal of expiratory airflow limitation at PEEP lower than 70–80% of intrinsic end-expiratory pressure (PEEPi), i.e. the end-expiratory alveolar pressure (PAet) without PEEP. It also shows the presence of an optimal PEEP. The optimal PEEP contributes to decrease PAet from 7.4 ± 0.9 (SD) to 5.4 ± 0.9 hPa (p –1.s (p –1.s (p < 0.0001; severe flow limitation). This simplistic mathematical model gives a plausible explanation of the expiratory airflow limitation removal with PEEP and a rationale to the practice of PEEP application to airflow limited patients. (shrink)
Over a period of more than twenty years, Sybil Wolfram gave lectures at Oxford University on Philosophical Logic, a major component of most of the undergraduate degree programmes. She herself had been introduced to the subject by Peter Strawson, and saw herself as working very much within the Strawsonian tradition. Central to this tradition, which began with Strawson's seminal attack on Russell's theory of descriptions in ‘On Referring' (1950), is the distinction between a sentence and what is said by (...) a sentence − Strawson initially called the latter a use of a sentence, and sometimes a proposition , but his most frequent term for what is said , which Wolfram consistently adopts, is the statement expressed.1 The force of the distinction is clearly illustrated in ‘On Referring', which uses it to undermine the common assumption that any sentence must be either true, or false, or meaningless. Russell had argued on this basis that a sentence such as ‘The King of France is bald' (which is clearly neither true nor meaningless) must be false, but Strawson points out that if we distinguish between the sentence itself and the statement that it expresses (on some occasion of use), we can quite easily combine the admission that the sentence is meaningful − for it can in appropriate circumstances be used to express true and false statements − with the claim that nevertheless if the circumstances are ‘inappropriate' (in particular, when there is no current King of France), the sentence can fail to express a statement that is either true or false. On this picture, therefore, it is sentences that are meaningful, but statements that are the primary bearers of truth. (shrink)
In responding to three reviews of Evolution in Four Dimensions (Jablonka and Lamb, 2005, MIT Press), we briefly consider the historical background to the present genecentred view of evolution, especially the way in which Weismann’s theories have influenced it, and discuss the origins of the notion of epigenetic inheritance. We reaffirm our belief that all types of hereditary information—genetic, epigenetic, behavioural and cultural—have contributed to evolutionary change, and outline recent evidence, mainly from epigenetic studies, that suggests that non-DNA heritable variations (...) are not rare and can be quite stable. We describe ways in which such variations may have influenced evolution. The approach we take leads to broader definitions of terms such as ‘units of heredity’, ‘units of evolution’, and ‘units of selection’, and we maintain that ‘information’ can be a useful concept if it is defined in terms of its effects on the receiver. Although we agree that evolutionary theory is not undergoing a Kuhnian revolution, the incorporation of new data and ideas about hereditary variation, and about the role of development in generating it, is leading to a version of Darwinism that is very different from the gene-centred one that dominated evolutionary thinking in the second half of the twentieth century. (shrink)
Sir Roger Penrose, retired professor of mathematics at the University of Oxford and collaborator with Stephen Hawking on black hole theory, has written 'a complete guide to the laws of the universe' called The Road to Reality. His publisher calls it the most important and ambitious work of science for a generation. Penrose caused a furore in the world of consciousness studies with his 1989 book The Emperor's New Mind, which conjectured a new mechanism for consciousness and kept a faithful (...) band of researchers busy for a decade with models based on microtubules and the like. Sadly, the idea fizzled out. The title of the 2002 Tucson 'Toward a Science of Consciousness' conference poetry slam winner was: Microtubules - my ass! (shrink)
In this paper I try to bring together two contexts in which the term “gene” is used. Perhaps this is overly hasty. But I’m trying to bring a term from an evolutionary context (“unexpressed genetic variation”) together with one from a developmental context (“constructed functional gene”).
Mind–body dualism has rarely been an issue in the generative study of mind; Chomsky himself has long claimed it to be incoherent and unformulable. We first present and defend this negative argument but then suggest that the generative enterprise may license a rather novel and internalist view of the mind and its place in nature, different from all of, (i) the commonly assumed functionalist metaphysics of generative linguistics, (ii) physicalism, and (iii) Chomsky’s negative stance. Our argument departs from the empirical (...) observation that the linguistic mind gives rise to hierarchies of semantic complexity that we argue (only) follow from constraints of an essentially mathematical kind. We assume that the faculty of language tightly correlates with the mathematical capacity both formally and in evolution, the latter plausibly arising as an abstraction from the former, as a kind of specialized output. On this basis, and since the semantic hierarchies in question are mirrored in the syntactic complexity of the expression involved, we posit the existence of a higher-dimensional syntax structured on the model of the hierarchy of numbers, in order to explain the semantic facts in question. If so, syntax does not have a physicalist interpretation any more than the hierarchy of number-theoretic spaces does. (shrink)
A traditional view maintains that thought, while expressed in language, is non-linguistic in nature and occurs in non-linguistic beings as well. I assess this view against current theories of the evolutionary design of human grammar. I argue that even if some forms of human thought are shared with non-human animals, a residue remains that characterizes a unique way in which human thought is organized as a system. I explore the hypothesis that the cause of this difference is a grammatical way (...) of structuring semantic information, and I present evidence that the organization of grammar precisely reflects the organization of a specific mode of thought apparently distinctive of humans. Since there appears to be no known non-grammatical structuring principle for the relevant mode of thought, I suggest that grammar is that principle, with no independent ?Language of Thought? needed. (shrink)
1. Pohlers and The Problem. I first met Wolfram Pohlers at a workshop on proof theory organized by Walter Felscher that was held in Tübingen in early April, 1973. Among others at that workshop relevant to the work surveyed here were Kurt Schütte, Wolfram’s teacher in Munich, and Wolfram’s fellow student Wilfried Buchholz. This is not meant to slight in the least the many other fine logicians who participated there.2 In Tübingen I gave a couple of (...) survey lectures on results and problems in proof theory that had been occupying much of my attention during the previous decade. The following was the central problem that I emphasized there: The need for an ordinally informative, conceptually clear, proof-theoretic reduction of classical theories of iterated arithmetical inductive definitions to corresponding constructive systems. As will be explained below, meeting that need would be significant for the then ongoing efforts at establishing the constructive foundation for and proof-theoretic ordinal analysis of certain impredicative subsystems of classical analysis. I also spoke in Tübingen about.. (shrink)
Contemporary arguments for forms of psycho-physical dualism standardly depart from phenomenal aspects of consciousness ('what it is like' to have some particular conscious experience). Conceptual aspects of conscious experience, as opposed to phenomenal or visual/perceptual ones, are often taken to be within the scope of functionalist, reductionist, or physicalist theories. I argue that the particular conceptual structure of human consciousness makes this asymmetry unmotivated. The argument for a form of dualism defended here proceeds from the empirical premise that (...) conceptual structure in a linguistic creature like us is a combinatorial and compositional system that implicates a distinction between simple and complex, or 'atomic' and 'molecular' concepts. The argument is that conceptual atoms, qua atoms, are irreducible to anything else. If so, and if the atoms are essentially semantic, a form of dualism follows: though positively inviting naturalistic inquiry into the semantic and mental aspects of nature, it requires that we look at the mental as a primitive domain of nature. Schematically, then, the argument is as follows: (1) Human consciousness/thought is conceptually structured. (2) The human conceptual system is a 'particulate' system at a syntactic and semantic level of representation (the notion of a 'particulate' system is developed in Section 2). (3) This implies the existence of conceptual 'particles', concepts that have no further semantic decomposition ('atoms'). (4) A conceptual atom cannot be explained in terms of anything that does not involve its own intrinsic properties (Section 3). (5) Physicalism as normally conceived is inconsistent with (3) and (4) (Section 4). (shrink)
Darwin proposed that evolutionary novelties are environmentally induced in organisms “constitutionally” sensitive to environmental change, with selection effective owing to the inheritance of constitutional responses. A molecular theory of inheritance, pangenesis , explained the cross‐generational transmission of environmentally induced traits, as required for evolution by natural selection. The twentieth‐century evolutionary synthesis featured mutation as the source of novelty, neglecting the role of environmental induction. But current knowledge of environmentally sensitive gene expression, combined with the idea of genetic accommodation of mutationally (...) and environmentally induced change, supports a revival of Darwin's original theory that is consistent with modern molecular and population genetics. †To contact the author, please write to: Smithsonian Tropical Research Institute, c/o Escuela de Biología, Universidad de Costa Rica, Costa Rica; e‐mail: firstname.lastname@example.org. (shrink)
Computers today are not only the calculation tools - they are directly (inter)acting in the physical world which itself may be conceived of as the universal computer (Zuse, Fredkin, Wolfram, Chaitin, Lloyd). In expanding its domains from abstract logical symbol manipulation to physical embedded and networked devices, computing goes beyond Church-Turing limit (Copeland, Siegelman, Burgin, Schachter). Computational processes are distributed, reactive, interactive, agent-based and concurrent. The main criterion of success of computation is not its termination, but the adequacy of (...) its response, its speed, generality and flexibility; adaptability, and tolerance to noise, error,faults, and damage. Interactive computing is a generalization of Turing computing, and it calls for new conceptualizations (Goldin, Wegner). In the info-computationalist framework, with computation seen as information processing, natural computation appears as the most suitable paradigm of computation and information semantics requires logical pluralism. (shrink)
Traditionally, Ancient Mesopotamian epistemic practices resulting in the vast corpus of cuneiform ‘lexical lists’ and other, similarly formatted treatises have been conceptualized as “ Listenwissenschaft ” in Assyriology. Introduced by the German Assyriologist Wolfram v. Soden in 1936 , this concept has also been utilized in other disciplines of the Humanities as a terminological means to describe epistemic activity allegedly inferior to ‘Western’ modes of analytical and hypotactic scientific reasoning. Building on the exemplary evidence of a bilingual list of (...) cuneiform compound graphemes from the early 2nd millennium BCE as well as on recent conceptualizations of ‘epistemic cultures’ and the instrumental function of material ‘representations’ in the context of epistemic practices, the present paper attempts to replace the essentialistic and teleological concept of an Ancient Mesopotamian “ Listenwissenschaft ” with a new epistemological model describing the underlying epistemic practices as highly adaptive non-linear epistemic practices comparable to what has been described as ‘practices with »epistemic things«’ in recent epistemology and practice theory. (shrink)
This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.
In 1675, Leibniz elaborated his longest mathematical treatise he everwrote, the treatise ``On the arithmetical quadrature of the circle, theellipse, and the hyperbola. A corollary is a trigonometry withouttables''. It was unpublished until 1993, and represents a comprehensive discussion of infinitesimalgeometry. In this treatise, Leibniz laid the rigorous foundation of thetheory of infinitely small and infinite quantities or, in other words,of the theory of quantified indivisibles. In modern terms Leibnizintroduced `Riemannian sums' in order to demonstrate the integrabilityof continuous functions. The (...) article deals with this demonstration,with Leibniz's handling of infinitely small and infinite quantities,and with a general theorem regarding hyperboloids. (shrink)
I argue that the implementation of theDummettian program of an ``anti-realist'' semanticsrequires quite different conceptions of the technicalmeaning-theoretic terms used than those presupposed byDummett. Starting from obvious incoherences in anattempt to conceive truth conditions as assertibilityconditions, I argue that for anti-realist purposesnon-epistemic semantic notions are more usefully kept apart from epistemic ones rather than beingreduced to them. Embedding an anti-realist theory ofmeaning in Martin-Löf's Intuitionistic Type Theory(ITT) takes care, however, of many notorious problemsthat have arisen in trying to specify suitableintuitionistic (...) notions of semantic value,truth-conditions, and validity, taking into accountthe so-called ``defeasibility of evidence'' forassertions in empirical discourses. (shrink)
The starting-point is the distinction between concept and conception. Our conceptions of gold, for instance, are the different understandings we get when we hear the word ‘gold’ whereas the concept of gold consists in the scientific determination of what gold is. It depends on the context whether it is more reasonable to claim a concept or to look for fitting conceptions. By arguing against metaphysical realism and for non-metaphysical realism, I will elaborate on some philosophical reasons for dealing with conceptions (...) instead of concepts of God, and secondly, I will discuss how such conceptions should be critically assessed. (shrink)
I analyze a number of the quantum no-signalling proofs (Ghirardi et al. 1980, Bussey 1982, Jordan 1983, Shimony 1985, Redhead 1987, Eberhard and Ross 1989, Sherer and Busch 1993). These purport to show that the EPR correlations cannot be exploited for transmitting signals, i.e., are not causal. First, I show that these proofs can be mathematically unified; they are disguised versions of a single theorem. Second, I argue that these proofs are circular. The essential theorem relies upon the tensor (...) product representation for combined systems, which has no physical basis in the von Neumann axioms. Historically, the construction of this representation scheme by von Neumann and Weyl built no-signalling assumptions into the quantum theory. Signalling between the wings of the EPR-Bell experiments is unlikely but is not ruled out empirically by the class of proofs considered. (shrink)
In the fall of 1990 I had just began my doc- toral studies at the University of Connecticut. Freshly arrived from Italy, I came to the United States to work with Carl Schlichting on something to do with phenotypic plastic- ity. I spent most of that semester discussing with other graduate students what I thought was a momentous paper by Mary Jane West- Eberhard (1989) in the Annual Review of Ecol- ogy and Systematics. That paper, entitled Phe- notypic Plasticity (...) and the Origins of Diversity, was a (quite lengthy) forerunner of the (also quite bulky) book I am reviewing now. Like the paper, this volume has the potential to be momentous in the development of our ideas on phenotypic evolution. (shrink)
Carnap took the content of a particular sentence or set of sentences to consist in the set ofthe consequences of the sentence or set. This claim equates meaning with inferential role, but it restricts the inferences to deductive or explicative ones. Here I reject a recent proposal by Rober Brandom, where inductive or ampliative inferences arealso meant to confer contents on expressions. I argue that if Brandom's inferentialist picture is upheld, and both explicative and ampliative inferences confer meaning, one consequence (...) of this is that the content of a sentence is to be read off from our ways of rationally altering our beliefs. Meaning and content then are largely concepts of pragmatics, with no clear theoretical interest. My critique affects certain aspects of Dummett's meaning-theoretic picture too,and the discussion also links up with the development of `dynamic semantics'. (shrink)
In view of the scope and scale of the latest scandals, e.g. Enron's maximum breaking bankruptcy, the re-discovery of ethics in business has received an impressive boost. By now even car salesmen have written ethics, a Code of Conduct, e.g. in the USA or Poland. But there is no clear aim of the role ethics obtains in organizational settings as we may show in some small cases of practical approaches to deal with ethics in organizations. We discuss how ethics is (...) the prerequisite to conduct any business and what advantages may be realized if a clear set of ethics is followed. We will discuss three practical examples. In cases of ethics-based values-added management of Siemens (Germany), Boeing (U.S.) and SAP (Germany) we explain the mechanisms of ethics in management to strengthen organizational success. We emphasize the importance of clear ethics-related communication processes in organizations. We explain the use of communication theories inside organizational processes to clarify communication about such an abstract topic as ethics. Finally, we point out how a management of ethical ideas and cultural values should be designed in business enterprises. (shrink)
Internalism is an explanatory strategy that makes the internal structure and constitution of the organism a basis for the investigation of its external function and the ways in which it is embedded in an environment. It is opposed to an externalist explanatory strategy, which takes its departure from observations about external function and mind-environment interactions, and infers and rationalizes internal organismic structure from that. This paper addresses the origins of truth, a basic ingredient in the human conceptual scheme. I suggest (...) the necessity of pursuing an internalist line of explanation for it, as adopted in the biolinguistic program and generative grammar at large. According to this view, the concept of truth is a presupposition for the way language is used in relation to the world, rather than a function of that use or a consequence of language-world relations. (shrink)
In 1661, Kaspar Schott published his comprehensive textbook Cursus mathematicus in Würzburg for the first time, his Encyclopedia of all mathematical sciences . It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred (...) authors, among them Protestants like Michael Stifel and Johannes Kepler, but also Catholics like Nicolaus Copernicus. The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra. (shrink)
The article deals with the Arabic sources of Chr. Clavius in Rome and the six different ways they were used by him in mathematics and astronomy. It inquires especially into his attitude towards al-Farghani, Thabit ibn Qurra, al-Bi[tdotu]ruji, Ibn Rushd, Mu[hdotu]ammad al-Baghdadi, Pseudo-Ibn al-Haytham, Jabir ibn Afla[hdotu], and Pseudo-al-[Tuotu]usi.
1. The Physical Church-Turing Thesis. Physicists often interpret the Church-Turing Thesis as saying something about the scope and limitations of physical computing machines. Although this was not the intention of Church or Turing, the Physical Church Turing thesis is interesting in its own right. Consider, for example, Wolfram’s formulation: One can expect in fact that universal computers are as powerful in their computational capabilities as any physically realizable system can be, that they can simulate any physical system . . (...) . No physically implementable procedure could then shortcut a computationally irreducible process. (Wolfram 1985) Wolfram’s thesis consists of two parts: (a) Any physical system can be simulated (to any degree of approximation) by a universal Turing machine (b) Complexity bounds on Turing machine simulations have physical signiﬁcance. For example, suppose that the computation of the minimum energy of some system of n particles takes at least exponentially (in n) many steps. Then the relaxation time of the actual physical system to its minimum energy state will also take exponential time. (shrink)
In a recent paper, Kit Fine offers a reconstruction of Cantor's theory of ordinals. It avoids certain mentalistic overtones in it through both a non-standard ontology and a non-standard notion of abstraction. I argue that this reconstruction misses an essential constructive and computational content of Cantor's theory, which I in turn reconstruct using Martin-Löf's theory of types. Throughout, I emphasize Kantian themes in Cantor's epistemology, and I also argue, as against Michael Hallett's interpretation, for the need for a constructive understanding (...) of Cantorian ?existence principles? (shrink)
Kant proclaimed that all theodicies must fail in ?On the Miscarriage of All Philosophical Trials in Theodicy?, but it is mysterious why he did so since he had developed a theodicy of his own during the critical period. In this paper, I offer an explanation of why Kant thought theodicies necessarily fail. In his theodicy, as well as in some of his works in ethics, Kant explained moral evil as resulting from unavoidable limitations in human beings. God could not create (...) finite beings without such limitations and so could not have created humans that were not prone to committing immoral acts. However, the work of Carl Christian Eberhard Schmid showed Kant that given his own beliefs about freedom and the nature of responsibility one could not account for moral evil in this way without tacitly denying that human beings were responsible for their actions. This result is significant not only because it explains an otherwise puzzling shift in Kant's philosophy of religion, but also because it shows that the theodicy essay provides powerful evidence that Kant's thinking about moral evil and freedom underwent fundamental shifts between early works such as the Groundwork and later works like the Religion within the Limits of Mere Reason. (shrink)
"Ethical Leadership" in modern multicultural corporations is first the consideration of different personal and cultural value systems in decision-making processes. Second, it is the assignment of responsibility either to individual or organisational causalities. The task of this study is to set the stage for a distinction between rational entities and the arbitrary preferences of individuals in economic decision making processes.Defining rational aspects of behaviour in economics will lead to the formal structures of organisational systems, which are independent of concrete but (...) varying values. Luhmann''s Theory of systems of communication describes the internal dynamic forces of economic communication processes in terms of formal structures. On the other hand Habermas'' Theory of discourse integrates the previous relationship between individual subjectivity and rational behaviour. Habermas gives an indication of how to separate subjective values and meaning from rational arguments in rational communication processes. The translation of these theoretical structures into practical applications for decision making processes and decision taking acts links the ethical, or value-oriented, context precisely to both individual and organisational areas of responsibility. (shrink)
Franchising in the business format sector accounted for approximately 35 percent of retail sales in the U.S. in 1991. Consequently, the franchising industry has a clear ethical responsibility to the public. At the same time, there exists an ethical obligation of the two major factors in the industry — the franchisor and the franchise — toward each other. Because the franchise agreement, which is the basis of the relationship, is originated by the franchisor, an asymmetrical distribution of power often exists, (...) resulting in opportunistic behavior by the franchisor. In other cases, questionable or unethical practices by franchisees likewise result in conflict. This paper examines some of the basic areas of the franchise relationship which result in conflict, and discusses the situation analysis in business format franchising, which shows promise for reduction of conflict and unethical behavior for the future. (shrink)
To understand adaptation (and exaptation), a more comprehensive view of development is required: one beyond a constraining force. Developmental plasticity may be an adaptation by natural selection simultaneously favored (or sometimes in conflict) at multiple levels of biological organization (e.g., cells, individuals, groups, etc.). To understand the interrelationships between developmental plasticity and adaptive evolution I borrow heavily from West-Eberhard (2003) and Frank (1995; 1997). Developmental plasticity facilitates evolution, results in particular patterns of evolutionary change, and may produce exaptations by (...) design rather than by chance. (shrink)
Ähnlich wie Adalbert Stifters Erzähler im Roman ,,Nachsommer” verband A. v. Humboldt auf seiner Amerikareise Erkundung und Erforschung, Reiselust und Erkenntnisstreben. Humboldt hat sein doppeltes Ziel klar benannt: Bekanntmachung der besuchten Länder, Sammeln von Tatsachen zur Erweiterung der physikalischen Geographie. Der Aufsatz ist in fünf Abschnitte gegliedert: Anliegen, Route, Methoden, Ergebnisse, Auswertung.
Currently, electronic agents are being designed and implemented that, unprecedentedly, will be capable of performing legally binding actions. These advances necessitate a thorough treatment of their legal consequences. In our paper, we first demonstrate that electronic agents behave structurally similar to human agents. Then we study how declarations of intention stated by an electronic agent are related to ordinary declarations of intention given by natural persons or legal entities, and also how the actions of electronic agents in this respect have (...) to be classified under German law. We discuss four different approaches of classifying agent declarations. As one of these, we propose the concept of an electronic person (i.e., agents with limited liability), enrolment of agents into an agent register, and agent liability funds as means to serve the needs of all contracting parties. (shrink)