An otherwise lawlike generalisation hedged by a ceteris paribus (CP) clause qualifies as a law of nature, if the CP clause can be substituted with a set of conditions derived from the multivariate regression model used to interpret the empirical data in support of the gen- eralisation. Three studies in human biology that use regression analysis are surveyed, showing that standard objections to cashing out CP clauses in this way—based on alleged vagueness, vacuity, or lack of testability—do not apply. CP (...) laws also cannot be said to be simply false due to the indefinitely many conditions not explicitly stated in their associated model: scientific CP clauses imply that these are, given the evidence, not nomically relevant. (shrink)

It is customary to divide Wittgenstein’s work into two broad phases, the first culminating in the Tractatus, and the second comprising the writings that began upon his return to philosophy in 1929 and culminating in the Investigations. It is also commonly assumed that the Tractatus propounds various doctrines concerning language and representation, doctrines which are repudiated in the later work, and often criticized explicitly. One problem with this view of the Trac- tatus is Wittgenstein’s claim in 6.54 that its propositions (...) are “nonsensical,”2 a claim which on its face is at odds with the idea that they present substantive philosophical theories. The usual way of handling this problem is to assume that the claim is not to be taken literally, that the sentences of the Tractatus are not nonsense in the sense of mere gibberish, but are intended somehow to engender in the attentive reader a grasp of certain important aspects of the relationship between language and the world. Beginning with her seminal paper “Throwing Away the Ladder,” Cora Diamond has proposed reading the Tractatus in a way that takes literally 6.54’s claim of the book’s nonsensicality, and rejects the idea that its sentences represent a kind of elevated nonsense intended to.. (shrink)

It is widely believed that some a priori necessary truths are not analytic in the sense of transformable by substitution of synonyms into logical truths. One much-cited example comes from the supposed incompatibility between colour predicates. The idea is that sentences like “Nothing is both blue all over (or uniformly or at a point) and also red” are not transformable into a logical truth in the same way as “Nothing is both a bachelor and married” because the requisite conceptual link (...) between “bachelor” and “not married” is absent between “blue” and “not red”. This paper examines whether colour exclusion may be more like the bachelor case than it initially appears. It transpires that the most promising line of thought is not, however, as has been argued at length in the literature, that “blue” in some more or less convoluted way manages to mean “not red”. Instead it is suggested that the requisite conceptual link may reside in the oft-ignored qualifications (“all over”, “uniformly”, etc.), without which there is no incompatibility in the first place. (shrink)

This paper is concerned with Wittgenstein's early doctrine of the independence of elementary propositions. Using the notion of a free generator for a logical calculus–a concept we claim was anticipated by Wittgenstein–we show precisely why certain difficulties associated with his doctrine cannot be overcome. We then show that Russell's version of logical atomism–with independent particulars instead of elementary propositions–avoids the same difficulties.

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

Although Wittgenstein’s most extensive discussion of aspect‐recognition appears in Part II of the Philosophical Investigations, aspect‐recognition was of interest to Wittgenstein almost from the beginning of his engagement with philosophy at Cambridge in 1912. However, the nature of that interest changes upon his return to Cambridge in 1929, and that change in turn is connected with the inter‐related ideas that philosophical clarity rests on recognising aspects of our grammar and that mathematical proof leads us to recognise new aspects of mathematical (...) expressions. (shrink)

ABSTRACT This paper offers an account of the early career of Martha Kneale, née Hurst, and of the five papers she published between 1934 and 1950. One on metaphysical and logical necessity, from 1938, is particularly interesting. In it she considers the metaphysics of time and offers an explanation of ‘the necessity of the past’, which has some resemblance to Kripke’s ideas about metaphysical necessities, in that it assigns an important role to experience in how we come to know them. (...) But Kneale’s view is very different from Kripke’s, depending not on doctrines about rigid designation but rather on recognition of the failure of the atomist/empiricist account of ‘simple’ and ‘complex’ concepts. That account cannot deal with such things as the relations of the determinates of a determinable like colour. A plausible corollary of this, which Kneale exploits, is that some of our experience reveals to us that there are phenomena which are intrinsically complex in having multiple distinguishable aspects, but where those aspects are inseparable. Other of the papers show Kneale to have been pursuing interesting lines of thought about McTaggart’s argument against the reality of time and on the mind-body problem. (shrink)

Wittgenstein’s phenomenological period is a subject to a variety of interpretations which give different answers to the questions why and when did the author of the Tractatus start doing phenomenology, when and why did he stop it and what meaning had it for him. In my paper I argue for the view that Wittgenstein tried to overcome difficulties of his early philosophy by applying phenomenological investigations loosely inspired by Mach. Firstly he assumed that they may be carried out as grammatical (...) investigations of the structure of a so­‑called phenomenological language. However, finally Wittgenstein came to the conclusion that such a language is impossible. Contrary to many interpreters I believe that the rejection of phenomenological language did not put an end to the whole Wittgenstein’s phenomenology, for it persisted thereafter for a couple of years in a form of investigations of grammatical invariants of the part of our ordinary language devised to express our sensual experience. (shrink)

Les Remarques philosophiques sont la première tentative de mettre en oeuvre le programme qui découle de l’échec du projet du Tractatus Logico-Philosophicus. Le noyau de ce programme est donné par l’abandon de l’analyse des nombres avancée dans le Tractatus. Wittgenstein se rend compte que les nombres doivent se trouver à la base même du langage, dans la structure des propositions élémentaires. En même temps, il se rend compte qu’il est impossible de fournir la logique sousjacente au langage avant d’avoir procédé (...) à l’analyse. Le projet d’une investigation logique des phénomènes s’imposait, donc, même après l’abandon de l’idée d’un langage phénoménologique. The Philosophical Remarks is a first attempt at pursuing the philosophical agenda determined by the failure of the Tractarian project. The central point of this agenda is the abandonment of the analysis of number that had been given in the Tractatus. Wittgenstein realizes that numbers should be brought back to the basis of language, as part of the structure of the elementary propositions themselves. At the same time, he realizes that it is impossible to give the logic underlying our language before the process of logical analysis is carried out. He undertakes the project of a logical investigation of phenomena even after giving up the idea of a phenomenological language. (shrink)

After the works of Jaako Hintikka, David Stern and, more recently, Denis Perrin, the idea that there is a wittgensteinian reflection upon the time and that it is at the origin of the abandonment of the project of a phenomenological language is nothing surprising, but we cannot consider it established yet. It seems to me that an important element in this debate is in chapter VII of the Philosophical Remarks : indeed, we find there the very first sustained discussion on (...) the possibility of a phenomenological language —a discussion obviously centred on the question of time. Without aiming to propose an “alternative” reading of Wittgenstein’ reflections on time and the phenomenological language, I would like to bring to light the importance of this chapter for this problem and also try to show that the interpretation key must be looked for in a reductio ad absurdum whose base is the impossibility to measure time. (shrink)

A conjecture on the metaphysical nature of Tractatus objects is put forward and its interpretative adequacy is tested. The clarification of the true import of the metaphor of logical space and the recognition of the theoretical role played by Wittgenstein's explicit claim that the emptiness of logical space is conceivable enable us to account for the thesis that objects are the substance of the world. Once objects are identified with those universal abstract entities which are qualia, and complexes or states (...) of affairs with their concrete instances, some statements of the Tractatus become liable to a consistent reading: that objects are colourless ; that space, time and colour are forms of objects ; that Leibniz's Principle of the Identity of Indiscernibles, though still holding for complexes, does not apply to objects . Lastly, it is shown how the interpretation of objects as qualia sheds a vivid light on the theme of the relation between objects and time. (shrink)

In Wittgenstein’s manuscripts dating from 1929 and 1930, there are a number of entries on the notion of probability. In this paper, I explore Wittgenstein’s manuscripts between October 1929 and March 1930 and demonstrate, first, that Wittgenstein completely rejects the assumption that probability statements are based on an a priori principle. Second, I argue that the standard interpretation, which claims that Wittgenstein adopts an ‘epistemological view’ of probability, significantly understates the importance of Wittgenstein’s development of the notion of hypotheses as (...) a philosophical term of art. (shrink)

The idea that the function of language is its use is commonly ascribed to the Later Wittgenstein. In this paper, I argue that there is textual evidence already coming from the early manuscripts proving that Wittgenstein's philosophical development is culminating in the idea of function as use around 1929–30. I interpret a passage from Ms‐107 in order to show that Wittgenstein's practical turn has sources in different stages of his philosophical development, each of which is dominated by different ideas: the (...) idea of a picture theory; the idea of a phenomenological language and the idea of function as use. (shrink)

The National Library of Finland and the Von Wright and Wittgenstein Archives at the University of Helsinki keep the collected correspondence of Georg Henrik von Wright, Wittgenstein’s friend and successor at Cambridge and one of the three literary executors of Wittgenstein’s Nachlass. Among von Wright’s correspondence partners, Elizabeth Anscombe and Rush Rhees are of special interest to Wittgenstein scholars as the two other trustees of the Wittgenstein papers. Thus, von Wright’s collections held in Finland promise to shed light on the (...) context of decades of editorial work that made Wittgenstein’s later philosophy available to all interested readers. In this text, we present the letters which von Wright received from Anscombe and Rhees during the first nine months after Wittgenstein’s death. This correspondence provides a vivid picture of the literary executors as persons and of their developing relationships. The presented letters are beautiful examples of what the correspondence as a whole has to offer; it depicts – besides facts of editing – the story of three philosophers, whose conversing voices unfold the human aspects of inheriting Wittgenstein’s Nachlass. Their story does not only deal with editing the papers of an eminent philosopher, but with the attempt to do justice to the man they knew, to his philosophy and to his wishes for publication. (shrink)

Using new archival material, this article reconstructs the editorial history of Philosophical Grammar, an edition that Rush Rhees crafted from Wittgenstein's papers. Contrasting the often‐held view that Rhees, in editing Philosophical Grammar, arbitrarily interfered with Wittgenstein's Big Typescript, the article illuminates the work, motives and reasons that underlie Rhees’ editing. Although recent philological evidence supports his editorial decisions, Rhees, at the time, made them based on his desire to do justice to his understanding of Wittgenstein's philosophical orientation. Against this background, (...) purely text‐philological criticism of Philosophical Grammar seems to come from a philosophical culture that was alien to Rhees. (shrink)

RESUMO O objetivo deste artigo é mostrar que as interpretações "tradicional" e "resoluta" não livraram o "Tractatus" da aparente autoderrota paradoxal. Argumento que essas leituras apresentam apenas uma nova roupagem ao paradoxo. A leitura "tradicional" de Hacker acaba atribuindo uma conspiração metafísica ao "Tractatus", o que é incompatível com os objetivos do livro. A leitura "resoluta" de Diamond e Conant atribui a Wittgenstein uma conspiração autoral, o que contradiz suas opiniões sobre autoria e método. Com base nas dificuldades encontradas em (...) ambos os lados do debate atual, concluo este artigo propondo vários requisitos que a correta interpretação do "Tractatus" deve preencher. (shrink)

To be a realist about modality, need one claim that more exists than just the various objects and properties that populate the world—e.g. worlds other than the actual one, or maximal consistent sets of propositions? Or does the existence of objects and properties by itself involve the obtaining of necessities (and possibilities) in re? The latter position is now unpopular but not unfamiliar. Aristotle held that objects have essences, and hence necessarily have certain properties. Recently it has been argued that (...) the identity of any property is tied to the natural laws in which it figures, which entails that the occurrence of properties involves the obtaining of nomological necessities ([24], pp. 206-33 and 234-60; [23]; cf. [25] and [6]). Somewhat less recently, Wittgenstein ([28], p. 168) worried that the reality of at least some properties—precise shades of colors being a prime example—involved the obtaining in re of certain impossibilities. This paper argues that Wittgenstein’s worries were right, and not just concerning some properties, but all properties whatever. That there are objects and properties in the world at all, then, amounts to there obtaining modal states of affairs. This argument supplements, rather than replaces, the others. The position on property incompatibility advanced here actually helps defend Aristotelian essentialism against epistemological objections, or so I have argued ([15]). And while this paper’s position on property incompatibility diverges from the idea that a property’s nomic profile is essential to it—more on this in the next section—it is at least compatible with the thought that the necessity involved in the laws of nature enters into ontology at the ground level. (shrink)

Peter Hacker defends an interpretation of the later Wittgenstein's notion of grammar, according to which the inherently general grammatical rules are sufficient for sense-determination. My aim is to show that this interpretation fails to account for an important contextualist shift in Wittgenstein's views on sense-determination. I argue that Hacker attributes to the later Wittgenstein a rule-based, combinatorial account of sense, which Wittgenstein puts forward in the Tractatus. I propose that this is not how we should interpret the later Wittgenstein because (...) he insists that particular circumstances of use play a necessary role in determining the boundary between sense and nonsense. (shrink)

A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that (...) emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. (shrink)

First I will explore the importance granted by Wittgenstein, in the middle period, to memory, in the primary/phenomenological world. According to him, memory is the source of time , past , knowledge and identity . The main objective of this article is to present Wittgenstein's reasons for the rejection of the phenomenological project, using as backdrop his analysis about time (and the abandonment of the semantical and epistemological roles granted to memory). For this purpose it will be crucial to understand (...) a false analogy, that according to him was the cause for the quest for an ideal language. This false analogy can be interpreted as the attribution of a mistaken status to memory (in the phenomenological sense), that leads to the illusion of a criteria of exactitude for the phenomenological description. At the end of this article, I will point out briefly the importance of those ideas to the understanding of the so called "private language argument". (shrink)

This paper aims to explain how the Tractatus attempts to unify logic by deriving the truth-functionality of logical necessity from the thesis that a proposition shows its sense. I first interpret the Tractarian notion of showing as the displaying of what is intrinsic to an expression (or a symbol). Then I argue that, according to the Tractatus, the thesis that a proposition shows its sense implies the determinacy of sense, the possibility of the complete elimination of non-primitive symbols, the analyticity (...) thesis and the strong analyticity thesis. The picture theory emerges as what provides the only acceptable account of an elementary proposition, subject to the constraint that a proposition must show its sense. The picture theory and the analyticity thesis then entail the contingency thesis (that an elementary proposition is contingent) and the independence thesis (that elementary propositions are mutually logically independent) which, together with the strong analyticity thesis, imply that all logical propositions are tautologies. (shrink)

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The condition is: (...) logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss, which goes back to Carruthers. And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many. (shrink)

Humeans have a problem with quantities. A core principle of any Humean account of modality is that fundamental entities can freely recombine. But determinate quantities, if fundamental, seem to violate this core principle: determinate quantities belonging to the same determinable necessarily exclude one another. Call this the problem of exclusion. Prominent Humeans have responded in various ways. Wittgenstein, when he resurfaced to philosophy, gave the problem of exclusion as a reason to abandon the logical atomism of the Tractatus with its (...) free recombination of elementary propositions. Armstrong promoted a mereological solution to the problem of exclusion; but his account fails in manifold ways to provide a general solution to the problem. Lewis studiously avoided committing to any one solution, trusting simply that, since Humeanism was true, there had to be some solution. Abandonment; failure; avoidance: we Humeans need to do better. -/- In this paper, I present what I take to be the best account of quantities, tailoring it where needed to meet Humean demands as well as my own prior commitment to quidditism, and my own comparativist inclinations. In short: determinables, not determinates, are the fundamental properties, and freely recombine; determinates arise from the instantiation of determinables in an enhanced world structure; determinate quantities may be local (in a sense to be explained), but they are not intrinsic. Is the account I end up with Humean? Not, unfortunately, as it stands: the problem of exclusion still rears its ugly head. After dismissing a failed attempt at a solution, I consider in the final section the two viable Humean options. One attributes the source of the necessary exclusions to conventional definition, the other attributes it to logic. The first is safe and familiar, but not a response I can accept given my other commitments. The second is more radical and less familiar; but I am convinced it is on the right track. I don’t have space to develop it much here, but I put it out for future research. (shrink)

Georg Wilhelm Friedrich Hegel (1770-1831) est probablement l’un des plus importants penseurs et philosophes de notre époque. On peut dire que les sciences humaines en général et la philosophie en particulier doivent prendre une position positive ou négative concernant la philosophie hégélienne avant de procéder à d’autres développements qui leur seraient propres. Plus précisément, ce collectif trouve sa racine dans une double urgence : les menaces des crises environnementale, politique et économique, les nouveaux enjeux qu’elles entraînent, d’une part, et l’absence (...) jusqu’à présent de réponses prometteuses, de l’autre. Il est temps de faire le point et de contribuer à fournir de nouvelles pistes de réflexion. Le présent ouvrage, bilingue, est le fruit de la collaboration d’éminents spécialistes internationaux qui ont répondu avec enthousiasme à notre invitation. Les 14 textes qui y sont réunis sont distribués selon trois thématiques et, tout en respectant la nature de la pensée hégélienne, leurs thèmes se chevauchent inévitablement. La première partie, « Aspects de la pensée de Hegel / Aspects of Hegel’s Thought », regroupe les textes qui discutent en profondeur d’un aspect de la pensée de Hegel, tout en analysant un enjeu qui se trouve dans ses propres œuvres. Les contributions de la deuxième partie, « Marx et Hegel / Marx and Hegel », examinent la relation entre ces deux philosophes. Comment faut-il comprendre les passages dans lesquels Marx accuse Hegel d’idéalisme, dont celui, largement cité, dans la préface du premier tome du Capital, n’est qu’un exemple? Dans la troisième partie, « Hegel à l’époque contemporaine / Hegel in Modern Times », les auteurs se penchent sur l’influence de la pensée de Hegel sur plusieurs penseurs. (shrink)

Resumo: Ludwig Wittgenstein tentou desenvolver, desde 1929, uma abordagem à filosofia da lógica em termos de escalas de medição. Embora mostrasse grande sensibilidade a diversos tipos de escalas, Wittgenstein não estava bem posicionado para fazer seu projeto render frutos, porque a teoria das medidas não começou a fazer avanços significativos antes do final da década de 1940, e continuou desfrutando de um progresso relevante, até os anos 80. Não obstante, nas suas obras e palestras dos anos 30, Wittgenstein fez diversas (...) tentativas de entender a lógica, ou a “gramática” da linguagem religiosa e ética relativa à medição. Este artigo é uma tentativa de desenvolver algumas dessas ideias que ocorreram a Wittgenstein, na sua fase intermediária, dentro do contexto da evolução posterior da teoria da medição. Especificamente, defende-se que as linguagens religiosa e ética são formas extremas de medição, não empíricas nem fatuais. Elas representam o caso-limite da medição.: Ludwig Wittgenstein attempted to develop an approach to the philosophy of logic in terms of measurement scales. While he showed great sensitivity to different kinds of scaling, Wittgenstein was not in a good position to bring this project to fruition; measurement theory did not begin to develop significantly until the late 1940s, and only made pertinent advances as late as the 1980s. However, in writings and lectures from the 1930s, Wittgenstein made a number of attempts to understand the logic, or “grammar”, of religious and ethical language in relation to measurement. This article is an attempt to develop some of these nascent ideas in intermediate Wittgenstein in terms of later developments in measurement theory. Specifically, it is argued that religious and ethical language are extreme forms of non-empirical and non-factual forms of measurement; they represent the limit-case of measurement. (shrink)

This article considers an interpretative model for the study of Heraclitus, which was first put forward by Alexander Mourelatos in 1973, and draws upon a related model put forward by Julius Moravcsik beginning in 1983. I further develop this combined model and provide a motivation for an interpretation of Heraclitus. This is also of interest for modern metaphysics due to the recurrence of structurally similar problems, including the ‘colour exclusion’ problem that was faced by Wittgenstein. Further, I employ the model (...) to shed new light on Heraclitus’ image of the river, while relating potential readings to various contemporary metaphysical views. (shrink)

This article is about the history of logic in Australia. Douglas Gasking (1911?1994) undertook to translate the logical terminology of John Anderson (1893?1962) into that of Ludwig Wittgenstein's (1921) Tractatus. At the time Gilbert Ryle (1900?1976), and more recently David Armstrong, recommended the result to students; but it is reasonable to have misgivings about Gasking as a guide to either Anderson or Wittgenstein. The historical interest of the debate Gasking initiated is that it yielded surprisingly little information about Anderson's traditional (...) (syllogistic or Aristotelian) logic and its relation to classical (first-order predicate or Russellian) logic, the ostensible topic; but the materials now exist to interpret Anderson's logic in classical logic, possibly as an algebra of classes. This would be of little interest to contemporary logicians, but it might shed some light on Anderson's philosophy. (shrink)

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...) B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

ABSTRACTIn 1931 Wittgenstein wrote: ‘the limit of language manifests itself in the impossibility of describing the fact that corresponds to a sentence without simply repeating the sentence’. Here, Wittgenstein claims, ‘we are involved … with the Kantian solution of the problem of philosophy’. This paper shows how this remark fits with Wittgenstein's early account of the substance of the world, his account of logic, and ultimately his view of philosophy. By contrast to the currently influential resolute reading of the Tractatus, (...) the paper argues that the early Wittgenstein did not aim at destroying the idea of a limit of language, but that the notion lies at the very heart of Wittgenstein's early view. In doing so, the paper employs and defends the Kantian interpretation of Wittgenstein's early philosophy. (shrink)

The problem of explaining color perception has fascinated painters, philosophers and scientists throughout the history. In many cases, the ideas and discoveries about color perception in one of these categories influenced the others, thus resulting in one of the most remarkable cross-fertilization of human thought. At the end of the nineteenth century, two models stood out as the most convincing ones: Young-Helmholtz’s trichromacy on one side, and Hering’s opponency on the other side. The former was mainly supported by painters and (...) scientists, although with some noticeable exceptions as, e.g., Otto Runge, while the majority of philosophers supported the latter. These two apparently incompatible models were proven to be two complementary parts of the hugely complex chain of events which leads to human color perception. Recently, a rigorous mathematical theory able to incorporate both trichromacy and opponency has been developed thanks to the use of the language and tools of quantum information. In this paper, we discuss the placement of this model within the philosophical theories about color. (shrink)

The perception involves a lot of enigmas, the unity between its content and form not always looking to be assured. Such enigmas are exemplified by the optical illusions, by Molyneux’s famous problem and also, as it interests us here, by the problem of the expression of colors in chromatic models, which express logical incompatibilities, but which refer to the territory of experience itself with colors and pigments. In this paper, we will distinguish two uses of Farbenoktaeder by Wittgenstein by registering (...) the difference, which we consider relevant, between ample incompatibility and restrict incompatibility among colors. (shrink)

A study in philosophical methodology aimed at providing a clear view of the scope and limits of philosophical inquiry.

The distinction between the a priori and the a posteriori is an old and influential one. But both the distinction itself and the crucial notion of a priori knowledge face powerful philosophical challenges. Many philosophers worry that accepting the a priori is tantamount to accepting epistemic magic. In contrast, this Element argues that the a priori can be formulated clearly, made respectable, and used to do important epistemological work. The author's conception of the a priori and its role falls short (...) of what some historical proponents of the notion may have hoped for, but it allows us to accept and use the notion without abandoning either naturalism or empiricism, broadly understood. This Element argues that we can accept and use the a priori without magic. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

I discuss the account of logical consequence advanced in Wittgenstein's Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein's claim that all propositions can be analysed as truth functions of elementary propositions.

It is argued that the Tractatus Project of Logical Atomism, in which the world is conceived of as the totality of independent atomic facts, can usefully be understood by conceiving of each fact as a bit in logical space. Wittgenstein himself thinks in terms of logical space. His elementary propositions, which express atomic facts, are interpreted as tuples of co-ordinates which specify the location of a bit in logical space. He says that signs for elementary propositions are arrangements of names. (...) Here, the names are understood as numerical symbols specifying coordinates. It is argued that, using this approach, the so-called colour-exclusion problem, which was Wittgensteins reason for abandoning the Tractatus, is in fact soluble. However, if logical space is a continuum then some coordinates will need to be expressed by numerical symbols that are infinite in size. How is this to be understood in Tractatus terms? It is shown that, in the Tractatus, Wittgenstein did recognise the possibility of infinite propositions and sentences expressing them. At first sight his approach to infinite sentences, and the approach of the present paper, seem to differ, but it is argued that the difference is superficial. Finally, we address the question of whether Logical Atomism is viable and this raises issues concerning its relationship to natural science. (shrink)

Statements of degree appear to falsify basic doctrines in Tractatus Logico-Philosophicus. I offer a fresh formulation of the challenge and assess a solution proposed on Wittgenstein’s behalf by Sarah Moss. I find that Moss’s proposal fails. The proposal rides in part on novel interpretations of pronouncements by Wittgenstein on the nature of the elementary proposition. I find that the interpretations cannot be sustained but that Moss’s textual case hints at important and overlooked features of the Tractarian program. I develop Wittgenstein’s (...) comparison of propositions to measuring instruments and apply it throughout, showing that it captures philosophical commitments in Tractatus that otherwise tend to slip from view. (shrink)

Logical structure may explain the necessity and a priori knowability of such truths as that if A is red then A is either red or green. But this explanation cannot be extended to sentences that, while necessary and knowable a priori, do not wear the appropriate logical structure on their sleeves – sentences like ''''if A is a point and A is red, then A is not green,'''' or ''''if A is a sphere, then A is not a cube.'''' The (...) real origin of these sentences'' necessity and a priori knowability is a relationship between the meanings of their component atomic sentences – a relationship which cannot be systematically reduced to logical structure by translating those atomic sentences into any kind of ''''ideal'''' language. Moreover, this kind of relationship is one to which any atomic sentences are susceptible if they have a classifying, or comparison-implying, content. Arguably, then, all atomic sentences are capable of being related to others in ways that are necessary and knowable a priori. (shrink)