The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which the green-hypothesis (...) is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (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)

After Tractatus Logico-Philosophicus, Wittgenstein realized that elementary propositions may logically conflict with each other, due to the fact that the most elementary measurements may contradict each other. This led to the view that logic consists of various calculi. A calculus consists of measurement scales, each scale being a rule for the application of numbers. These scales determine logical relationships between elementary propositions by reason of arithmetical relations. Attempts to reject Wittgenstein's change in viewpoint, which ignore the relevance of measurement and (...) arithmetic, are remiss. In this light, I discuss Sarah Moss’s criticism of intermediate Wittgenstein. (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)

Intuitivamente, la realidad está formada por entidades y hechos existentes y concretos. Sin embargo, nuestro lenguaje y pensamiento versa también sobre hechos meramente posibles, sobre cosas inexistentes y entidades abstractas. ¿Cómo es esto posible? ¿Significa ello que cuando hablamos y pensamos de estas otras cosas no hablamos de nada real? ¿o mas bien la realidad está mas poblada de lo que pensábamos y hay diferentes maneras de formar parte de la realidad además de la de existir de manera positiva y (...) concreta? En este libro trataremos de arrojar luz a estas y otras preguntas similares, poniendo atención a las estrategias argumentativas generales que suelen esgrimirse en esta rama de la filosofía. (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)

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)

The aim of this paper is to offer some philosophical remarks concerning the concept of moral application in applied ethics. In doing so, I argue in favour of a philosophical approach towards applied ethics as a unitary form of moral experience. In fact every form of applied ethics, no matter how specific, moves from a problem of application and tries to fill a gap between moral theory and practice. This essential unity of applied ethics as a moral phenomenon is of (...) great philosophical interest, since it belongs to the core problem from which moral thinking itself originates. For this reason, what applied ethics may reveal to a philosophical inquiry could provide valuable insight into the nature of moral experience itself. This is why it is important to reflect on what applied ethics is and whether the way in which application is usually framed be ts the properties of moral experience or not. In the first section I submit some preliminary remarks concerning the theoretical requirements to any philosophical approach to applied ethics. In the second section I present how application is commonly understood in the applied ethics debate by discussing the deductive and the procedural models of application. Both models, however, draw upon a technological conception of application which fails to t the structure of moral experience. Finally, I brie y sketch out the main features and the future tasks of what seems to me to be the most promising approach to the issue, i.e., the hermeneutic concept of application. (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)

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)

One of the reasons colours, or better the conceptual organisation of the colour system, could be relevant to the philosophy of logic is that they necessitate some mutilation of truth tables by restricting truth functionality. This paper argues that the so-called ‘Colour Exclusion Problem’, the first great challenge for Wittgenstein’s Tractatus, is a legitimate philosophical motivation for a systematic mutilation of truth tables. It shows how one can express, through these mutilations, some intensional logical relations usually expressed by the Aristotelian (...) Square of Oppositions, as contrariety and subcontrariety. (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)

Study of Wittgenstein's claim in the Preface of the Tractatus that his thoughts are unassailably true and his declaration at the end of the work that his propositions are nonsensical.

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)

In the present work are identified the main features of the algebraic structure with respect to the logical operations, of the set of all the quantum mechanical utterances for which can be specified a factual counterpart and factual rules for truth valuation. This structure is found not to be a lattice. It depends crucially on the spacetime features of the operations by which the observer prepares the studied states and performs measurements on them.

In the first part of this paper, I argue against the view that laws of nature are contingent, by attacking a necessary condition for its truth within the framework of a conception of laws as relations between universals. I try to show that there is no independent reason to think that universals have an essence independent of their nomological properties. However, such a non-qualitative essence is required to make sense of the idea that different laws link the same universals in (...) different possible worlds. In the second part, I give a positive argument for the necessity of at least some laws of nature, by showing with the example of a paradigmatic law of association that it consists in an internal relation between two universals which are determinables of the same class of determinates, where this relation is essential to both. Furthermore, I show that the necessity of laws of association could be accommodated within David Lewis' Humean metaphysics, but that it is incompatible with David Armstrong's combinatorialism. (shrink)

It is commonly held that Wittgenstein abandoned the Tractatus largely because of a problem concerning color incompatibility. My aim is to solve this problem on Wittgenstein’s behalf. First I introduce the central program of the Tractatus (§1) and the color incompatibility problem (§2). Then I solve the problem without abandoning any Tractarian ideas (§3), and show that given certain weak assumptions, the central program of the Tractatus can in fact be accomplished (§4). I conclude by distinguishing my system of analysis (...) from others and by explaining the historical underpinnings of my understanding of the nature of elementary propositions (§5). (shrink)

Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.

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.

Argues for a causal-psychological account of acting for reasons. This view is distinguished from a more ambitious causal theory of action, clarified as far as possible, and motivated—against non-reductive, teleological, and behaviourist alternatives—on broadly metaphysical grounds.

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)

This paper provides an overview of the history of the notion of essence in 20th century analytic philosophy, focusing on views held by influential analytic philosophers who discussed, or relied on essence or cognate notions in their works. It in particular covers Russell and Moore’s different approaches to essence before and after breaking with British idealism, the (pre- and post-)logical positivists’ critique of metaphysics and rejection of essence (Wittgenstein, Carnap, Schlick, Stebbing), the tendency to loosen the notion of logical necessity (...) to accommodate certain metaphysical truths in Wittgenstein and others, Quine’s logical rehabilitation of metaphysics and criticism of de re modality, the modal view of essence promoted by the development of quantified modal logic (C. I. Lewis, Barcan Marcus, Kripke) and direct reference theory (Barcan Marcus, Kripke, Putnam), and the emergence of the notion of metaphysical necessity (Kneale, Kripke), and finally Fine’s re-establishment of a Neo-Aristotelian, hyperintensional notion of essence in contemporary metaphysics. (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)

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)

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)

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)

del's appeal to mathematical intuition to ground our grasp of the axioms of set theory, is notorious. I extract from his writings an account of this form of intuition which distinguishes it from the metaphorical platonism of which Gödel is sometimes accused and brings out the similarities between Gödel's views and Dummett's.

Philosophical Investigations, Volume 44, Issue 4, Page 372-402, October 2021.

One can attack a philosophical claim by identifying a misuse of the language used to state it. I distinguish between two varieties of this strategy: one belonging to Norman Malcolm and the other to Ludwig Wittgenstein. The former is flawed and easily dismissible as misled linguistic conservatism. It muddies the name of ordinary language philosophy. I argue that the latter avoids this flaw. To make perspicuous the kind of criticism of philosophical claims that the second variety makes available, I draw (...) a comparison between Wittgenstein’s recommendation that philosophers study ordinary language and Alfred Schütz’s recommendation that social scientists study the methods of the agents they study. Both do so in an attempt to sensitise philosophers and social scientists respectively to particular artefacts of method which can be easily mistaken for features of that which is studied. (shrink)

In this paper, I explore Wittgenstein’s inheritance of one specific strand of Kant’s criticism, in the Critique of Pure Reason, of reason’s inherent pretensions to totality. This exploration reveals new critical possibilities in Wittgenstein’s own philosophical method, challenging existing interpretations of Wittgenstein’s political thought as “conservative” and exhibiting the closeness of its connection to another inheritor of Kant’s critique of totality, the Frankfurt school’s criticism of “identity thinking” and the reification of reason to which it leads. Additionally, it shows how (...) Wittgenstein’s linguistic philosophy offers to challenge and undermine, in a historically novel way, the metaphysical assumptions underlying some of our most characteristic and ubiquitous social practices. (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)

The contemporary Humean programme that seeks to combine property realism with the denial of necessary connections between distinct existences is flawed. Objects and properties by their very natures are entangled in such connections. It follows that modal notions cannot be reductively analysed by appeal to the concept property, not even if the reducing theory posits an abundant supply of entities to fall under that concept.

Over a period of several decades spanning the origin of the Vienna Circle, Schlick repeatedly attacked Husserl''s phenomenological method for its reliance on the ability to intuitively grasp or see essences. Aside from its significance for phenomenologists, the attack illuminates significant and little-explored tensions in the history of analytic philosophy as well. For after coming under the influence of Wittgenstein, Schlick proposed to replace Husserl''s account of the epistemology of propositions describing the overall structure of experience with his own account (...) based on the structure of language rather than on the intuition of essences. I discuss both philosophers'' accounts of the epistemology of propositions describing the structure of experience. For both philosophers, this epistemology was closely related to the general epistemology of logic; nevertheless, neither philosopher had a completely coherent account of it. Comparison of the two approaches shows that perennial and severe theoretical obstacles stand in the way of giving an epistemology of the structure of experience, a central requirement for both philosophers'' theories. Consideration of these obstacles sheds a new light on the reasons for the historically decisive split between the continental and the analytic traditions, as well as on the subsequent development of the analytic tradition away from the structural description of experience. (shrink)

El presente artículo analiza las primeras consideraciones de Ludwig Wittgenstein respecto de la percepción de figuras ambiguas, lo que posteriormente fue englobado por la más amplia noción de “percepción de aspectos”. El objetivo consiste en poner de manifiesto algunas las consideraciones del Tractatus Logico-Philosophicus respecto al carácter intrínsecamente representacional de la percepción en el caso del Cubo de Necker, para establecer de qué manera y en qué medida sus primeras observaciones críticas de la percepción de propiedades que admiten grados en (...) Some Remarks on Logical Form, en 1929, puede impactar análogamente sobre su propia descripción de esta clase particular de experiencias bajo consideración. (shrink)

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)

This book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus , and the impact he had on Wittgenstein's later philosophical insights.

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)

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)

ABSTRACTWittgenstein’s remark that one cannot follow a rule only once has generated two puzzles: how can everyone accept it to be true? and why does Wittgenstein advance it? These two puzzles have tormented commentators for decades. In this paper I put forward a new interpretation and explain away the two puzzles. I shall show that Wittgenstein’s remark is plain truth and that his motivation behind making it is to dissolve the picture theory of meaning propounded in the Tractatus. This interpretation (...) also helps us to see that Wittgenstein’s other remark, that to follow a rule is a custom, is also a grammatical one. (shrink)

It is often held that Wittgenstein had to introduce numbers in elementary propositions due to problems related to the so-called colour-exclusion problem. I argue in this paper that he had other reasons for introducing them, reasons that arise from an investigation of the continuity of visual space and what Wittgenstein refers to as ‘intensional infinity’. In addition, I argue that the introduction of numbers by this route was prior to introducing them _via_ the colour-exclusion problem. To conclude, I discuss two (...) problems that Wittgenstein faced in the writings before _Some Remarks on Logical Form _, problems that are independent of the colour-exclusion problem but dependent on the introduction of numbers in elementary propositions. (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.