In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the publication of Hilbert's Grundlagen.We are particularly interested in the interrelations between the Italian and the German schools (mainly the (...) influence of Staudt's and Klein's works). We try also to understand the reason of the steady decline of the Italian school during the twentieth century. (shrink)

In un saggio del 1984 destinato a una certa fortuna interpretativa, lo storico dell’architettura Jean-Louis Cohen presentava la figura dell’architetto-intellettuale come l’esito di condizioni specifiche che avevano permesso ad alcuni architetti italiani – in contrapposizione, per esempio, a quelli francesi – di affiancare alla propria attività professionale e di insegnamento una riflessione approfondita sulle condizioni del proprio operare, rafforzando un’interpretazione dell’architettura com...

Debates about new technologies, such as crop and food genetic modification, raise pressing questions about the ways ‘experts’ and ‘ nonexperts’ communicate. These debates are dynamic, characterized by many voices contesting numerous storylines. The discoursal features, including language choices and communication strategies, of the GM debate are in some ways taken for granted and in others actively manipulated by participants. Although there are many voices, some have more influence than others. This study makes use of 50 hours of in-depth interviews (...) with GM scientists, nonexperts, and other stakeholders in the GM debate to examine this phenomenon. We uncover rhetorical devices used by scientists to characterize and ultimately undermine participation by non-experts in areas including rationality, knowledge, understanding and objectivity. Scientists engage with ‘the public’ from their own linguistic and social domain, without reflexive confirmation of their own status as part of the public and the citizenry. This raises a number of interesting ironies and contradictions, which are explored in the article. As such, it provides valuable insights into an increasingly important type of discourse. (shrink)

The world as perceived by human beings is full of colour. The world as described by physical scientists is composed of colourless particles and fields. Philosophical theories of colour since the scientific revolution have been primarily driven by a desire to harmonize these two apparently conflicting pictures of the world. Any adequate theory of colour has to be consistent with the characteristics of colour as perceived without contradicting the deliverances of the physical sciences. Given this conception of the aim of (...) a theory of colour, there are three possibilities for resolving the apparent conflict between the scientific and perceptual facts. The first possibility is to deny that physical objects have colours. Theories of this kind admit that objects appear coloured but maintain that these appearances are misleading. The conflict is resolved by removing colour from the external world. Second, it might be that colour is a relational property. For an object to possess a particular colour it must be related in the right way to a perceiver. One common version of this view analyzes colour as a disposition to cause particular kinds of perceptual experiences in a human being. Since the physical sciences deal only with the intrinsic properties of physical objects and their relations to other physical objects and not their relations to perceiving subjects, the possibility of conflict is removed. A third possible response to the conflict is to maintain that colour really is a property of external objects and that the conflict is merely apparent. Some theories of this form maintain that colour is identical to a physical property of objects. Others maintain that colour is a property that physical objects possess over and above all their physical <blockquote> 1 </blockquote> properties. Philosophical discussions of colour typically take the form of either elaborating on one of these three possibilities or attempting to show more generally that one of these three types of responses is to be preferred to the others.. (shrink)

Colour has often been supposed to be a subjective property, a property to be analysed orretly in terms of the phenomenological aspects of human expereince. In contrast with subjectivism, an objectivist analysis of color takes color to be a property objects possess in themselves, independently of the character of human perceptual expereince. David Hilbert defends a form of objectivism that identifies color with a physical property of surfaces - their spectral reflectance. This analysis of color is shown to provide (...) a more adequate account of the features of human color vision than its subjectivist rivals. The author's account of colro also recognises that the human perceptual system provides a limited and idiosyncratic picture of the world. These limitations are shown to be consistent with a realist account of colour and to provide the necessary tools for giving an analysis of common sense knowledge of color phenomena. (shrink)

Die Leitgedanken meiner Untersuchungen über die Grundlagen der Mathematik, die ich - anknüpfend an frühere Ansätze - seit 1917 in Besprechungen mit P. BERNAYS wieder aufgenommen habe, sind von mir an verschiedenen Stellen eingehend dargelegt worden. Diesen Untersuchungen, an denen auch W. ACKERMANN beteiligt ist, haben sich seither noch verschiedene Mathematiker angeschlossen. Der hier in seinem ersten Teil vorliegende, von BERNAYS abgefaßte und noch fortzusetzende Lehrgang bezweckt eine Darstellung der Theorie nach ihren heutigen Ergebnissen. Dieser Ergebnisstand weist zugleich die Richtung (...) für die weitere Forschung in der Beweistheorie auf das Endziel hin, unsere üblichen Methoden der Mathematik samt und sonders als widerspruchsfrei zu erkennen. Im Hinblick auf dieses Ziel möchte ich hervorheben, daß die zeit weilig aufgekommene Meinung, aus gewissen neueren Ergebnissen von GÖDEL folge die Undurchführbarkeit meiner Beweistheorie, als irrtüm lich erwiesen ist. Jenes Ergebnis zeigt in der Tat auch nur, daß man für die weitergehenden Widerspruchsfreiheitsbeweise den finiten Stand punkt in einer schärferen Weise ausnutzen muß, als dieses bei der Be trachtung der elementaren Formallsmen erforderlich ist. Göttingen, im März 1934 HILBERT Vorwort zur ersten Auflage Eine Darstellung der Beweistheorie, welche aus dem HILBERTschen Ansatz zur Behandlung der mathematisch-logischen Grundlagenpro bleme erwachsen ist, wurde schon seit längerem von HILBERT ange kündigt. (shrink)

This volume presents two Leibnizian writings, the Specimen of Philosophical Questions Collected from the Law and the Dissertation on Perplexing Cases. These works, originally published in 1664 and 1666, constitute, respectively, Leibniz's thesis for the title of Master of Philosophy and his doctoral dissertation in law. Besides providing evidence of the earliest development of Leibniz's thought and amazing anticipations of his mature views, they present a genuine intellectual interest, for the freshness and originality of Leibniz's reflections on a striking variety (...) of logico-philosophical puzzles drawn from the law. The Specimen addresses puzzling issues resulting from apparent conflicts between law and philosophy (the latter broadly understood as comprising also mathematics, as well as empirical sciences). The Dissertation addresses cases whose solution is puzzling because of the convoluted logical form of legal dispositions and contractual clauses, or because of conflicting priorities between concurring parties. In each case, Leibniz dissects the problems with the greatest ingenuity, disentangling their different aspects, and proposing solutions always reasonable and sometimes surprising. And he does not refrain from peppering his intellectual acrobatics with some humorous comments. bbbbbb. (shrink)

Debates about new technologies, such as crop and food genetic modification, raise pressing questions about the ways ‘experts’ and ‘ nonexperts’ communicate. These debates are dynamic, characterized by many voices contesting numerous storylines. The discoursal features, including language choices and communication strategies, of the GM debate are in some ways taken for granted and in others actively manipulated by participants. Although there are many voices, some have more influence than others. This study makes use of 50 hours of in-depth interviews (...) with GM scientists, nonexperts, and other stakeholders in the GM debate to examine this phenomenon. We uncover rhetorical devices used by scientists to characterize and ultimately undermine participation by non-experts in areas including rationality, knowledge, understanding and objectivity. Scientists engage with ‘the public’ from their own linguistic and social domain, without reflexive confirmation of their own status as part of the public and the citizenry. This raises a number of interesting ironies and contradictions, which are explored in the article. As such, it provides valuable insights into an increasingly important type of discourse. (shrink)

According to the most common interpretation of the simulation argument, we are very likely to live in an ancestor simulation. It is interesting to ask if some families of simulations are more likely than others inside the space of all simulations. We argue that a natural probability measure is given by computational complexity: easier simulations are more likely to be run. Remarkably this allows us to extract experimental predictions from the fact that we live in a simulation. For instance we (...) show that it is very likely that humanity will not achieve interstellar travel and that humanity will not meet other intelligent species in the universe, in turn explaining the Fermi's Paradox. On the opposite side, experimental falsification of any of these predictions would constitute evidence against our reality being a simulation. (shrink)

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...) wesentlichen Teil mit dadurch bedingt, daB es gelang, einen brauchbaren und leistungsfahigen Fonnalismus zu finden. - Was durch die Formel­ sprache in der Mathematik erreicht wird, das solI auch in der theoretischen Logik durch diese erzielt werden, namlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten konnen. Der Dbergang zu logischen Folgerungen, wie er durch das SchlieBen geschieht, wird in seine letzten Elemente zerlegt und erscheint als fonnale Umgestaltung der Ausgangsfonneln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem LogikkalkUl. Dieser Kalkiil macht die erfolgreiche Inangriffnahme von Problemen moglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehort z. B. (shrink)

§30. Significance of Desargues's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 CHAPTER VI. PASCAL'S THEOREM. §31. ...

A sensible quality is a perceptible property, a property that physical objects (or events) perceptually appear to have. Thus smells, tastes, colors and shapes are sensible qualities. An egg, for example, may smell rotten, taste sour, and look cream and round.1,2 The sensible qualities are not a miscellanous jumble—they form complex structures. Crimson, magenta, and chartreuse are not merely three different shades of color: the first two are more similar than either is to the third. Familiar color spaces or color (...) solids capture, to a greater or lesser extent, these relations between the colors. The same goes for sensible qualities perceived in other modalities: middle C, high C, and D are not merely three different notes, and the taste of lemons, oranges, and sugar cubes are not merely three different tastes. How can this structure of appearance be explained? One idea is that sensible qualities are of two sorts: basic and derived. The basic sensible qualities are the building blocks from which the derived sensible qualities can be.. (shrink)

The material contained in the following translation was given in substance by Professor Hilbertas a course of lectures on euclidean geometry at the University of G]ottingen during the wintersemester of 1898-1899. The results of his investigation were re-arranged and put into the formin which they appear here as a memorial address published in connection with the celebration atthe unveiling of the Gauss-Weber monument at G]ottingen, in June, 1899. In the French edition, which appeared soon after, Professor Hilbert made some (...) additions, particularly in the concludingremarks, where he gave an account of the results of a recent investigation made by Dr. Dehn.These additions have been incorporated in the following translation.Geometry, like arithmetic, requires for its logical development only a small number ofsimple, fundamental principles. These fundamental principles are called the axioms ofgeometry. The choice of the axioms and the investigation of their relations to one anotheris a problem which, since the time of Euclid, has been discussed in numerous excellentmemoirs to be found in the mathematical literature.1 This problem is tantamount to thelogical analysis of our intuition of space. (shrink)

There are serious reasons for accepting each of these propositions individually but there are apparently insurmountable difficulties with accepting all three of them simultaneously if we assume that color is a single property. 1) and 2) together seem to imply that there is some property which all organisms with color vision can see and 3) seems to imply that there can be no such property. If these implications really are valid then one or more of these propositions will have to (...) be rejected in spite of whatever reasons can be given for their apparent acceptability. Before going on to discuss possible resolutions of this apparent contradiction it is worth pointing out there our three propositions are not all of a kind. Proposition 1) is a metaphysical thesis about the ontological status of color and proposition 3) is an empirical thesis about what properties organisms with color vision are capable of detecting. If you accept 1) then 2) will appear to verge on the trivial, but if 1) is denied then the status of 2) will appear more problematic. In what follows I will have more to say about why we either should or should not accept all three of these propositions. (shrink)

The typical kind of color realism is reductive: the color properties are identified with properties specified in other terms (as ways of altering light, for instance). If no reductive analysis is available — if the colors are primitive sui generis properties — this is often taken to be a convincing argument for eliminativism. That is, realist primitivism is usually thought to be untenable. The realist preference for reductive theories of color over the last few decades is particularly striking in light (...) of the generally anti-reductionist mood of recent philosophy of mind. The parallels between the mind—body problem and the case of color are substantial enough that the difference in trajectory is surprising. While dualism and non-reductive physicalism are staples, realist primitivism is by and large a recent addition to the color literature. And it remains a minority position, although one that is perhaps gaining support. In this paper, we investigate whether it should be accepted, and conclude it should not be. (shrink)

New genetic technologies promise to generate valuable insights into the aetiology of several psychiatric conditions, as well as a wider range of human and animal behaviours. Advances in the neurosciences and the application of new brain imaging techniques offer a way of integrating DNA analysis with studies that are looking at other biological markers of behaviour. While candidate 'genes for' certain conditions, including schizophrenia and bipolar disorders, are said to be 'un-discovered' at a faster rate than they are discovered, many (...) studies are being conducted on personality traits such as aggressiveness and anti-social traits. The clinical applicability and implications of these studies are often discussed within the scientific community. However, little attention has so far been paid to their possible policy implications in relation to criminality management and to Criminal Law itself. Similarly, the related ethical issues arising in the field of crime control, and the tensions between enhancing security for society and protecting civil liberties, are currently under-explored. This paper investigates these ethical issues by focusing on the views of those professionals – including judges, lawyers, probation officers and social workers – who work with individuals 'deemed at risk' of violent and aggressive behaviours. It also discusses and problematizes mainstream rhetoric and arguments around the notion of 'risky individuals'. (shrink)

If you trained someone to emit a particular sound at the sight of something red, another at the sight of something yellow, and so on for other colors, still he would not yet be describing objects by their colors. Though he might be a help to us in giving a description. A description is a representation of a distribution in a space (in that of time, for instance).

Larry Hardin has been the most steadfast and influential critic of physicalist theories of color over the last 20 years. In their modern form these theories originated with the work of Smart and Armstrong in the 1960s and 1970s1 and Hardin appropriately concentrated on their views in his initial critique of physicalism.2 In his most recent contribution to this project3 he attacks Michael Tye’s recent attempts to defend and extend color physicalism.4 Like Byrne and Hilbert5, Tye identifies color with the (...) reflecting properties of objects (“reflectance physicalism”). Specifically, the determinate and determinable colors are identified with types of reflectances. (Setting some complications aside, the reflectance of an object is the proportion of light that it reflects at each wavelength in the visible spectrum.) These reflectance types are, in the terminology of Hilbert, anthropocentric—in the terminology of Lewis6, they are not very “natural”. (shrink)

When we open our eyes, the world seems full of colored opaque objects, light sources, and transparent volumes. One historically popular view, _eliminativism_, is that the world is not in this respect as it appears to be: nothing has any color. Color _realism_, the denial of eliminativism, comes in three mutually exclusive varieties, which may be taken to exhaust the space of plausible realist theories. Acccording to _dispositionalism_, colors are _psychological_ dispositions: dispositions to produce certain kinds of visual experiences. According (...) to both _primitivism_ and _physicalism_, colors are not psychological dispositions; they differ in that primitivism says that no reductive analysis of the colors is possible, whereas physicalism says that they are physical properties. This paper is a defense of physicalism about color. (shrink)

"This admirable volume of readings is the first of a pair: the editors are to be applauded for placing the philosophy of color exactly where it should go, in ...

Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.

We can start with a definition. “[C]olour constancy is the constancy of the perceived colours of surfaces under changes in the intensity and spectral composition of the illumination.” (Foster et al. 1997) Given the definition we can now ask a question: Does human color vision exhibit color constancy?1 The answer to the question depends in part on how we interpret it. If the question is understood as asking whether human color vision displays constancy for every possible scene across every possible (...) illumination then the answer is no.2 If the question is understood as asking whether human color vision displays some degree of constancy for some scenes across some range of illuminants then the answer is yes. The more interesting questions involve characterizing the degree of constancy human vision displays, the types of scenes and ranges of illuminants for which approximate constancy can be achieved and the.. (shrink)

Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...) wesentlichen Teil mit dadurch bedingt, daB es gelang, einen brauchbaren und leistungsfahigen Fonnalismus zu finden. - Was durch die Formel­ sprache in der Mathematik erreicht wird, das solI auch in der theoretischen Logik durch diese erzielt werden, namlich eine exakte, wissenschaftliche Behandlung ihres Gegenstandes. Die logischen Sachverhalte, die zwischen Urteilen, Begriffen usw. bestehen, finden ihre Darstellung durch Formeln, deren Interpretation frei ist von den Unklarheiten, die beim sprachlichen Ausdruck leicht auftreten konnen. Der Dbergang zu logischen Folgerungen, wie er durch das SchlieBen geschieht, wird in seine letzten Elemente zerlegt und erscheint als fonnale Umgestaltung der Ausgangsfonneln nach gewissen Regeln, die den Rechenregeln in der Algebra analog sind; das logische Denken findet sein Abbild in einem LogikkalkUl. Dieser Kalkiil macht die erfolgreiche Inangriffnahme von Problemen moglich, bei denen das rein inhaltliche Denken prinzipiell versagt. Zu diesen gehort z. B. (shrink)

Edward Wilson Averill By the phrase 'anthropocentric account of color' I mean an account of color that makes an assumption of the following form: two ...

Much of the current genetic research into aggressive and violent behaviour focuses on young people and might appear to offer the hope of targeted prediction and intervention. In the UK data is collected on children from various agencies and collated to produce ‘at risk of offending’ identities used to justify intervention. Information from behavioural genetic tests could conceivably be included. Regulatory frameworks for collecting, storing and using information from DNA samples differ between the health service and the police particularly in (...) the need for consent and the treatment of children. This paper draws on discussions with professionals involved with ‘problem’ young people to consider their views on the utility of genetic research for tackling violent/aggressive behaviour and the impact an identification of genetic susceptibility might have on their clients. (shrink)