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)

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. ...

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)

Erster Teil Die übliche Auffassung von der Mathematik und ihre Widerlegung.- 1 Die Rolle von Anschauung und Erfahrung.- 2 Die Rolle der Voraussetzungen.- 3 Die Nichtuntrüglichkeit des mathematischen Schliessens.- Zweiter Teil Die landläufige Auffassung von der Physik und ihre Berichtigung.- 4 Physikalische Begriffsbildungen.- 5 Die Gesetze der Physik und ewige Naturgesetze.- 6 Die Beziehung zwischen Theorie und Experiment.- Dritter Teil Fragen philosophischen Charakters.- 7 Physikalische Gesetzlichkeit und Kausalität.- 8 Naturgeschehen und Wahrscheinlichkeit.- 9 Die Rolle von idealen Gebilden.

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)

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)

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)

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 ...

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 ...

Color-vision defects constitute a spectrum of disorders with varying degrees and types of departure from normal human color vision. One form of color-vision defect is dichromacy; by mixing together only two lights, the dichromat can match any light, unlike normal trichromatic humans, who need to mix three. In a philosophical context, our titular question may be taken in two ways. First, it can be taken at face value as a question about visible properties of external objects, and second, it may (...) be interpreted as the more intangible question of “what it’s like” to be color-blind. (shrink)

These volumes will serve as useful resources for anyone interested in philosophy of color perception or color science.

The target article is an attempt to make some progress on the problem of color realism. Are objects colored? And what is the nature of the color properties? We defend the view that physical objects (for instance, tomatoes, radishes, and rubies) are colored, and that colors are physical properties, specifically types of reflectance. This is probably a minority opinion, at least among color scientists. Textbooks frequently claim that physical objects are not colored, and that the colors are "subjective" or "in (...) the mind." The article has two other purposes: first, to introduce an interdisciplinary audience to some distinctively philosophical tools that are useful in tackling the problem of color realism and, second, to clarify the various positions and central arguments in the debate. (shrink)

A survey of arguments for and against the view that colors are physical properties.

Although it has been something of a fetish for philosophers to distinguish between hallucination and illusion, the enduring problems for philosophy of perception that both phenomena present are not essentially different. Hallucination, in its pure philosophical form, is just another example of the philosopher’s penchant for considering extreme and extremely idealized cases in order to understand the ordinary. The problem that has driven much philosophical thinking about perception is the problem of how to reconcile our evident direct perceptual contact with (...) objects and properties with the equally evident fact that there is no phenomenological signal separating error and truth. “The obscure object of hallucination” offers a subtle and plausible solution to this problem and one that solves the problem generally, not just in the special case of hallucination. Johnston’s objective is to offer a theory of perception that meets two constraints: (1) that it provide an explanation of the possibility of delusive and veridical sensings that are indistinguishable from the first-person perspective and (2) that it count as form of direct realism where this is taken to involve acquaintance with the objects of perception. Johnston uses the first constraint to rule out disjunctivism. The second constraint is used to rule out conjunctivism, which as Johnston uses the term, includes most of the widely adopted philosophical theories of perception. Johnston also develops his own sophisticated and interesting theory of perception. In what follows, I will discuss the relation of Johnston’s theory to conjunctivism, examine one of his anti-conjunctivist arguments and finally compare Johnston’s theory with some other versions of direct realism. These topics constitute a very incomplete selection of the important issues discussed in this rich and interesting paper. I will also not disagree, in any fundamental way, with any of the central theses of Johnston’s discussion.. (shrink)

A survey of color science and color vision.

The Dangerous Book for Boys Abstract: Seventeenth and eighteenth century discussions of the senses are often thought to contain a profound truth: some perceptible properties are secondary qualities, dispositions to produce certain sorts of experiences in perceivers. In particular, colors are secondary qualities: for example, an object is green iff it is disposed to look green to standard perceivers in standard conditions. After rebutting Boghossian and Velleman’s argument that a certain kind of secondary quality theory is viciously circular, we discuss (...) three main lines of argument for the secondary quality theory. The first is inspired by an intuitively compelling picture of perception articulated by Reid; the second is that the secondary quality theory is a conceptual truth; the third line of argument is presented in Johnston’s influential paper ‘How to speak of the colors’. We conclude that all these arguments fail, and that the secondary quality theory is unmotivated. Keywords: color, secondary quality, disposition, vision, perception.. (shrink)

This article addresses the question of how, if at all, citizens can sustain an effective sense of political belonging without sacrificing other sources of ethical identity. We begin with a critical analysis of Rousseau's classic considerations of politics and religion, which concludes that membership of a sub-political ethical community is incompatible with an effective sense of political belonging. This critique leads us to a consideration of the basic character of contemporary constitutional-democratic polities (drawing on the work of James Tully) and (...) of Waldron's account of the circumstances of politics. These considerations are developed into the claim that we can identify two sources of political belonging: recognition and acknowledgement - which correspond to two aspects of democratic citizenship: as status and as mode of being. On the basis of this claim, we argue that an effective sense of political belonging can be compatible with membership of sub-political ethical communities iff members of the political community are characterised by the majoritarian virtue of civic responsiveness and the minoritarian virtue of civic endurance. We sketch the character of these virtues and the relationship to one another in arguing that only the widespread presence of both kinds of virtue is sufficient to secure citizens' confidence in the polity and hence its stability. (shrink)

Our reply is in three parts. The first part concerns some foundational issues in the debate about color realism. The second part addresses the many objections to the version of physicalism about color ("productance physicalism") defended in the target article. The third part discusses the leading alternative approaches and theories endorsed by the commentators.

One of the traditional problems of philosophy is the nature of the connection between perceptual experience and empirical knowledge. That there is an intimate connection between the two is rarely doubted. Three case studies of visual deficits due to brain damage are used to motivate the claim that perceptual experience is neither necessary nor sufficient for perceptual knowledge. Acceptance of this claim leaves a mystery as to the epistemic role, if any, of perceptual experience. It is argued that one function (...) of perceptual experience is to provide information about the sources of beliefs, both as to which perceptual modality and within a given modality. This information is useful in assessing the reliability of perceptual beliefs. (shrink)