I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)

I argue that it is possible and useful for moral philosophy to provide surveyable representations of moral vocabulary. I proceed in four steps. First, I present two dominant interpretations of the concept “surveyable representation”. Second, I use these interpretations as a background against which I present my own interpretation. Third, I use my interpretation to support the claim that Wittgenstein’s “Lecture on Ethics” counts as an example of a surveyable representation. I conclude that, since the lecture qualifies as a surveyable (...) representation, it is possible to provide surveyable representations of moral vocabulary. Fourth, I argue that it is useful for contemporary moral philosophy to provide surveyable representations, because it may help to dissolve problems in current debates. I provide an example of such a debate, namely, the debate between cognitivists and non-cognivitists. (shrink)

The concept of übersichtliche Darstellung is of fundamental significance for Wittgenstein . Hacker translates übersichtliche Darstellung as ‘surveyable representation’ and equates it with the tabulation of grammar. He asks what surveyability means, whether examples can be found in Wittgenstein’s work, and why this method characterizes the form of account he gives. Ultimately, however, Hacker is unable to answer these questions and he attributes this failure to Wittgenstein. This paper argues that it is Hacker’s interpretation that fails, and presents an alternate (...) understanding of übersichtliche Darstellung ; one that enables us to answer Hacker’s questions in a manner consistent with Wittgenstein’s philosophical practices. Normal 0 false false false EN-US X-NONE X-NONE. (shrink)

Recent work on dispositions offers a new solution to the long-running dispute about whether explanations of intentional action are causal explanations. The dispute seemed intractable because of a lack of percipience about dispositions and a commitment to Humean orthodoxies about causation on both sides.

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

In this paper, I will defend the claim that there are three existence properties: the second-order property of being instantiated, a substantive first-order property (or better a group of such properties) and a formal, hence universal, first-order property. I will first try to show what these properties are and why we need all of them for ontological purposes. Moreover, I will try to show why a Meinong-like option that positively endorses both the former and the latter first-order property is the (...) correct view in ontology. Finally, I will add some methodological remarks as to why this debate has to be articulated from the point of view of reality, i.e., by speaking of properties, rather than from the point of view of language, i.e., by speaking of predicates (for such properties). (shrink)

Between April and November 1912, Bertrand Russell and Ludwig Wittgenstein were engaged in a joint philosophical program. Wittgenstein‘s meeting with Gottlob Frege in December 1912 led, however, to its dissolution – the joint program was abandoned. Section 2 of this paper outlines the key points of that program, identifying what Russell and Wittgenstein each contributed to it. The third section determines precisely those features of their collaborative work that Frege criticized. Finally, building upon the evidence developed in the preceding two (...) sections, section 4 recasts along previously undeveloped lines Wittgenstein‘s logical–philosophical discoveries in the two years following his encounter with Frege in 1912. The paper concludes, in section 5, with an overview of the dramatic consequences the Frege-Wittgenstein critique had for Russell‘s philosophical development. (shrink)

The unpleasantness of pain motivates action. Hence many philosophers have doubted that it can be accounted for purely in terms of pain’s possession of indicative representational content. Instead, they have explained it in terms of subjects’ inclinations to stop their pains, or in terms of pain’s imperative content. I claim that such “noncognitivist” accounts fail to accommodate unpleasant pain’s reason-giving force. What is needed, I argue, is a view on which pains are unpleasant, motivate, and provide reasons in virtue of (...) possessing content that is indeed indicative, but also, crucially, evaluative. (shrink)

In the early-to-mid 1930s, Wittgenstein investigated solipsism via the philosophy of language. In this paper, I want to reopen Wittgenstein's ‘grammatical’ examination of solipsism.Wittgenstein begins by considering the thesis that only I can feel my pains. Whilst this thesis may tempt us towards solipsism, Wittgenstein points out that this temptation rests on a grammatical confusion concerning the phrase ‘my pains’. In Section 1, I unpack and vindicate his thinking. After discussing ‘my pains’, Wittgenstein makes his now famous suggestion that the (...) word ‘I’ has two distinct uses: a subject-use and an object-use. The purpose of Wittgenstein's suggestion has, however, been widely misunderstood. I unpack it in Section 2, explaining how the subject-use connects with a phenomenological language, and so again tempts us into solipsism. In Sections 3–4, I consider various stages of Wittgenstein's engagement with this kind of solipsism, culminating in a rejection of solipsism via reflections on private languages. (shrink)

This paper argues for two major revisions in the way philosophers standardly think of vision science and vision theories more generally. The first concerns mental representations and the second supervenience. The central result is that the way is cleared for an externalist theory of perception. The framework for such a theory has what are called Aristotelian representations as elements in processes the well-functioning of which is the principal object of a theory of vision.

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the (...) bounds of logic as formal ontology of abstract objects. (shrink)

The way physics and other parts of science work can be explained in the framework of radical constructivism. However, this constructivist view itself shows that a uniquily accepted epistemology, constructivism or any other, would not be an advantage for the developmentof science. Unlike physics some parts of science successfully use constructivist concepts inside their theories. Because this is the case particularly in learning theory, constructivist ideas can help to improve physics teaching.

Desire satisfaction has not received detailed philosophical examination. Yet intuitive judgments about the satisfaction of desires have been used as data points guiding theories of desire, desire content, and the semantics of ‘desire’. This paper examines desire satisfaction and the standard propositional view of desire. Firstly, I argue that there are several distinct concepts of satisfaction. Secondly, I argue that separating them defuses a difficulty for the standard view in accommodating desires that Derek Parfit described as ‘implicitly conditional on their (...) own persistence’, a problem posed by Shieva Kleinschmidt, Kris McDaniel, and Ben Bradley. The solution undercuts a key motivation for rejecting the standard view in favour of more radical accounts proposed in the literature. (shrink)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

Ordinary cases of object seeing involve the visual perception of space and spatial location. But does seeing an object require such spatial perception? An empirical challenge to the idea that it does comes from reflection upon Bálint's syndrome, for some suppose that in Bálint's syndrome subjects can see objects without seeing space or spatial location. In this article, I question whether the empirical evidence available to us adequately supports this understanding of Bálint's syndrome, and explain how the aforementioned empirical challenge (...) can be resisted. (shrink)

In On Certainty, §166, Wittgenstein mentions the difficulty of realizing the “groundlessness of our believing.” In the course of reviewing what makes this realization so difficult, I examine a certain way of understanding one of Wittgenstein's techniques for getting us to realize it, his use of the “hinge” metaphor. It implies that hinge-propositions possess that status inherently; for some commentators, this is because of their connection to instinctive and habitual behaviours. I offer an alternative interpretation of the remarks that have (...) been used to support this understanding that better explains their role in Wittgenstein's response to scepticism and other epistemological problems. (shrink)

Kant, Wittgenstein, and Husserl all held that visual awareness of objects requires visual awareness of the space in which the objects are located. There is a lively debate in the literature on spatial perception whether this view is undermined by the results of experiments on a Balint’s syndrome patient, known as RM. I argue that neither of two recent interpretations of these results is able to explain RM’s apparent ability to experience motion. I outline some ways in which each interpretation (...) may respond to this challenge, and suggest which way of meeting the challenge is preferable. I conclude that RM retains some awareness of the larger space surrounding the objects he sees. (shrink)

The article examines Wittgenstein’s thought on the language of pain in first and third person. Relevant grammatical differences, according to the typical analytical method of this philosopher, are highlighted not only in relation to the two perspectives, but also regarding the use of cognitive verbs such as ‘feeling’ and ‘knowing’. The exam of many texts suggests some issues concerning the relationship between personal experiences, empathic grasping of other’s feelings and their conceptual translation. A brief comparison with some Thomas Aquinas’ texts (...) complements the proposal of the existence of non intentional knowledge. (shrink)

Cora Diamond has recently criticised as mere legend the interpretation of a quip of Ramsey's, contained in the epigraph below, which takes him to be objecting to or rejecting Wittgenstein's Tractarian distinction between saying and showing. Whilst I agree with Diamond's discussion of the legend, I argue that her interpretation of the quip has little evidential support, and runs foul of a criticism sometimes made against intuitionism. Rather than seeing Ramsey as making a claim about the nature of propositions, as (...) Diamond does, we should understand him as making a claim about the grammar of the logical connectives. Such a view coheres with the extant evidence of the nature of Wittgenstein's and Ramsey's 1929 philosophical encounters. It is also compatible with attributing to Ramsey a recognition of Wittgenstein's distinction and with denying that criticising it is the lesson of the quip. (shrink)

Here, the logical behaviour of negation in Wittgenstein's Tractatus is compared with Demos' account of denial. Even if we hold negation as a pure syntactical device, at least in some context, it brings a handful of complex semantic information – potentially an infinite amount. We advocate then the existence of at least two negations due to the existence of two different and non-reducible types of exclusion. The first negation is a Tractarian and classical one, based on the notion of contradiction, (...) whereas the second is a non-classical negation, based on the notion of contrariety. (shrink)

Many philosophers have held that it is not possible to experience a spatial object, property, or relation except against the background of an intact awareness of a space that is somehow ‘absolute’. This paper challenges that claim, by analyzing in detail the case of a brain-damaged subject whose visual experiences seem to have violated this condition: spatial objects and properties were present in his visual experience, but space itself was not. I go on to suggest that phenomenological argumentation can give (...) us a kind of evidence about the nature of the mind even if this evidence is not absolutely incorrigible. (shrink)

How should we think about the role of visual spatial awareness in perception and perceptual knowledge? A common view, which finds a characteristic expression in Kant but has an intellectual heritage reaching back farther than that, is that an account of spatial awareness is fundamental to a theory of experience because spatiality is the defining characteristic of “outer sense”, of our perceptual awareness of how things are in the parts of the world that surround us. A natural counterpart to this (...) idea is to treat self-consciousness as residing in a kind of sense that is fundamentally “inner”, such as introspection or whatever else gives one privileged access to his own mental states as well as the proprioceptive and kinesthetic awareness of bodily position. This division is compatible, of course, with the idea that inner sense provides an awareness of a distinctive kind of “body space”, but it treats that as importantly different from the awareness of the worldly space around one. -/- In contrast to such a picture, this dissertation proposes an account of visual spatial awareness according to which it is no less a source of self-consciousness than of the awareness of the objects around us, and an account of self-awareness in which visual experience is essentially implicated. I begin by arguing that we should think of visual spatial awareness not as necessary for the individuation of visual sensations but rather as an essential element in the awareness of an experientially objective world. In the subsequent chapters, I argue that in being visually aware of the egocentric positions of the worldly objects around us we are often aware also of our own spatial locations with respect to them, and that the visual experience of the world around one and one’s own situation in it is often an essential component in the knowledge that a human agent will have of his own intentional actions. (shrink)

It is sometimes objected that anti-individualism, because of its assumption of the constitutive role of natural and social environments in the individuation of intentional attitudes, raises sceptical worries about first-person authority--that peculiar privilege each of us is thought to enjoy with respect to non-Socratic self-knowledge. Gary Ebbs believes that this sort of objection can be circumvented, if we give up metaphysical realism and scientific naturalism and adopt what he calls a “participant perspective” on our linguistic practices. Drawing on broadly Wittgensteinian (...) considerations, I argue that Ebbs is right about this, and I show how two likely objections to his view can be circumvented. I also argue that mere adoption of the participant perspective does not serve to refute external-world sceptic. (shrink)

The paper argues that an internal debate within Wittgensteinian philosophy leads to issues associated rather with the later philosophy of Martin Heidegger. Rush Rhees's identification of the limitations of the notion of a “language game” to illuminate the relation between language and reality leads to his discussion of what is involved in the “reality” of language: “anything that is said has sense-if living has sense, not otherwise.” But what is it for living to have sense? Peter Winch provides an interpretation (...) and application of Rhees's argument in his discussion of the “reality” of Zande witchcraft and magic in “Understanding a Primitive Society”. There he argues that such sense is provided by a language game concerned with the ineradicable contingency of human life, such as (he claims) Zande witchcraft to be. I argue, however, that Winch's account fails to answer the question why Zande witchcraft can find no application within our lives. I suggest that answering this requires us to raise the question of why Zande witchcraft “fits” with their other practices but cannot with ours, a question of “sense” which cannot be answered by reference to another language game. I use Joseph Epes Brown's account of Native American cultures (in Epes Brown 2001) as an exemplification of a form of coherence that constitutes what we may call a “world”. I then discuss what is involved in this, relating this coherence to a relation to the temporal, which provides an internal connection between the senses of the “real” embodied in the different linguistic practices of these cultures. I relate this to the later Heidegger's account of the “History of Being”, of the historical worlds of Western culture and increasingly of the planet. I conclude with an indication of concerns and issues this approach raises, ones characteristic of “Continental” rather than Wittgensteinian philosophy. (shrink)

In recent years, philosophers have used expressions of Wittgenstein’s (e.g. “language-games,” “form of life,” and “family resemblance”) in attempts to conceive of the discipline of philosophy in a broad, open, and perhaps global way. These Wittgenstein-inspired approaches indicate an awareness of the importance of cultural and historical diversity for approaching philosophical questions. While some philosophers have taken inspiration from Wittgenstein in embracing contextualism in philosophical hermeneutics, Wittgenstein himself was more instrumental than contextual in his treatment of other philosophers; his focus (...) in his writings was on his own philosophical problems. Does this mean that Wittgensteinian philosophy is a poor resource after all for comparative, cross-cultural, or globally-engaged philosophy (i.e. if it is properly Wittgensteinian)? In this article, I examine the relevance of Wittgenstein to contextually-sensitive philosophy through studies of his conceptions of history and culture, his interest in Spengler’s philosophy of history, and recent scholarship by Hans-Johann Glock and Hans Sluga on the place of contextualism in Wittgenstein’s analysis of philosophical problems. Ultimately, this article advances the view that there are strong resources in Wittgenstein’s philosophy for those seeking a more globally-engaged approach to the field. (shrink)

According to A-theories of time, the metaphysical ground of change and dynamicity is provided by a continuous shifting in which events are past, present and future (A-determinations). It is often claimed that these theories make better sense of our experience of dynamicity than their rival, the B-theories; according to the latter, dynamicity is grounded solely in the irreducible earlier-than relations (B-relations) which obtain between events or states of affairs. In this paper, I argue that the experience of time's dynamicity, on (...) the contrary, cannot be accounted for solely in terms of representations of irreducible A-determinations, because any representation which is adequate to ground these experiences must itself involve representation of irreducible B-relations, while it needs not involve representation of A-determinations. Even if, as a matter of contingent fact, our experiences of dynamicity consisted of representations of successions of A-determinations, what would account for them being experiences of dynamicity would be solely the B-theoretic relations of succession, rather than the irrelevant A-theoretic nature of the relata. (shrink)

Is “good” a family-resemblance concept? Wittgenstein holds it is, since cases of goodness may not have anything in common, but there may be a continuous transition from some cases to others. Von Wright and Hacker argue it is not. They hold that family-resemblance concepts satisfy two conditions that goodness does not satisfy. I assess their arguments and then present a constitutivist account of goodness that Wittgenstein seems to endorse. The constitutivist account is what one would expect if goodness was a (...) family-resemblance concept. Finally, I note that Wittgenstein's nod towards non-descriptivism in the Investigations is paralleled by Stevenson's ethical emotivism. (shrink)

This paper offers a reconstruction of Wittgenstein's discussion on inductive proofs. A "algebraic version" of these indirect proofs is offered and contrasted with the usual ones in which an infinite sequence of modus pones is projected.

This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...) remarks on _Lebensformen_ is offered which factors in his reading of Alan Turing’s “On computable numbers, with an application to the _Entscheidungsproblem_“, as well as his discussions with Turing 1937-1939. An interpretation of the five occurrences of _Lebensform_ in the PI is then given in terms of a logical “regression” to _Lebensform_ as a fundamental notion. This regression characterizes Wittgenstein’s mature answer to the question, “What is the nature of the logical?”. (shrink)

Das obras de Newton da Costa, muitas pessoas na França conhecem apenas o renascimento da paraconsistência. Apresentamos algumas razões em defesa de investigações nessa parte da lógica. Acima de tudo, porém, relembramos uma das maiores contribuições de Newton da Costa: sua demonstração, em 1991, em colaboração com Doria, da indecidibilidade gödeliana do movimento na física matemátcia, um resultado que foi de certa forma previsto, por outras razões, por Duhem em 1906. DOI: 10.5007/1808-1711.2011v15n1p7.

The main question addressed by this article is this: How should one understand the role of the sentences of the Tractatus, given Wittgenstein’s statement that they are nonsensical? I begin with a presentation of three general principles of interpretation in order to avoid answering the question in an inappropriate way. I then move on to a short presentation and commentary on a selection of readings – namely, the ineffabilist, resolute and elucidatory ones – and elaborate the answers given by advocates (...) of these to the question explored here. I agree on many points with resolute and elucidatory readings: the Tractatus presents an austere conception of nonsense, and is not a book that seeks to present ontological or semantic theories. I point out, however, that these readings cannot fully explain the nature of Tractarian elucidations. Then I discuss those parts of the Tractatus which refer to the sentences of the book itself. The main proposal of my own approach is this: Tractarian elucidations should be construed as rules of translation, in that they show how to substitute certain expressions for others. They enable us to construct a notation in which everything that is expressible in ordinary language can be said perspicuously. (shrink)

What we observe, through our usually limited lens, is that differential growing of space determines forms -characterized by their shape, size and coloration. As non-Euclidean geometrical mathematics have proclaimed: forms are manifestations of the curvature of space. Physics and other natural laws impose mathematical structural restrictions to biological forms. The molecules comprising any living form become arranged in specific ways in response to physical forces as well as chemical and biochemical conditions. Over time, such forms inherit additional historical restrictions that (...) make up their meaning, their semiotics. Color does not escape from this orthogenic reality. In this study, we present the colored pattern of the connexivum of Triatoma maculata, an insect vector of the etiologic agent of Chagas disease. This model is used as an example to appreciate mimicry under a heterodox and provocative approach. We unveil that beyond 1) mathematical and 2) historical semiotic restrictions of T. maculata mimesis of a yellowish-black alternating pattern, there are also 3) artistic interpretations; where metaphysics of life, beyond human perspective, is included. (shrink)

El presente trabajo explora la posible afinidad de método entre las obras de Walter Benjamin y Ludwig Wittgenstein. El intento por parte de Benjamin de desarrollar un nuevo método de representación histórica gravita en torno a la categoría de “origen”, la cual sostiene sus más importantes trabajos de investigación histórica. En paralelo al trabajo de Benjamin, Wittgenstein dedicó una especial atención al problema de una exposición filosófica de los fenómenos, en especial en sus investigaciones sobre el lenguaje, a través de (...) categorías como la “representación perspicua” o la “visión de aspectos”. La filiación común de la reflexión de ambos autores en la morfología de Goethe nos permitirá definir el perfil de un posible enfoque estético para la investigación filosófica, dirigida a captar la generalidad de los fenómenos sin renunciar a salvaguardar su singularidad única. (shrink)

According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...) in fact, reasonable and related to Gödel’s proof. (shrink)

This work is an investigation into philosophical method and rational argument in moral philosophy. It makes an original contribution to human understanding, by taking some of the tools and techniques that Gordon Baker identifies in the later work of Wittgenstein, and using them as a way of fending for oneself in an area of philosophy that neither Baker, nor Wittgenstein, wrote on. More specifically, a discussion of some different aspects of the contemporary literature on Dancy’s moral particularism is used as (...) a vehicle for illustrating how Baker’s therapeutic conception of philosophy offers alternative possibilities for how we can do philosophy, and what counts as rational argument in moral philosophy. I maintain that, by considering some indicative ways in which Baker’s therapeutic approach to philosophy can dissolve, rather than solve, the kinds of perplexities found in the existing literature on Dancy’s moral particularism, we can liberate ourselves from the traditional/theoretical view of how we ought to do philosophy, and an understanding of rational argument in moral philosophy, to which we need not be committed. (shrink)

In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept (...) of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems. (shrink)

When it comes to Wittgenstein's philosophy of mathematics, even sympathetic admirers are cowed into submission by the many criticisms of influential authors in that field. They say something to the effect that Wittgenstein does not know enough about or have enough respect for mathematics, to take him as a serious philosopher of mathematics. They claim to catch Wittgenstein pooh-poohing the modern set-theoretic extensional conception of a real number. This article, however, will show that Wittgenstein's criticism is well grounded. A real (...) number, as an 'extension', is a homeless fiction; 'homeless' in that it neither is supported by anything nor supports anything. The picture of a real number as an 'extension' is not supported by actual practice in calculus; calculus has nothing to do with 'extensions'. The extensional, set-theoretic conception of a real number does not give a foundation for real analysis, either. The so-called complete theory of real numbers, which is essentially an extensional approach, does not define (in any sense of the word) the set of real numbers so as to justify their completeness, despite the common belief to the contrary. The only correct foundation of real analysis consists in its being 'existential axiomatics'. And in real analysis, as existential axiomatics, a point on the real line need not be an 'extension'. (shrink)

In this paper I explore a neglected discussion of vagueness put forward by Wittgenstein in his Philosophical Grammar (1932–34). In this work, unlike Philosophical Investigations (1953), Wittgenstein not only discusses the venerable Sorites paradox but provides a novel conception of vagueness using an analogy with coin tossing and converging intervals. As he sees it, the problematic picture of vagueness arises because we conflate aspects of the functioning of vague concepts with those of non-vague ones. Thus, while we accept that vague (...) concepts have no sharp cut-off points (are boundaryless), we nevertheless retain the idea that we can progress towards the penumbra the way we progress towards the cut-off points of non-vague concepts. As a potential remedy, Wittgenstein's analogy with coin tossing and converging intervals replaces this picture and provides an understanding of the functioning of vague concepts in which no notion of a progression arises. (shrink)

The aim of this paper is twofold. Firstly, it analyses the similarities that stem from Wittgenstein’s (Philosophical Investigations (1953)) and Brandom’s (Making it Explicit (1994)) commitment to pragmatics in the philosophy of language to account for moral utterances. That is, the study of the meaning of moral utterances is carried out resorting to the study of the acts being performed in producing or exhibiting these utterances. Both authors offer, therefore, a pragmatic solution in order to account for the meaning of (...) our moral vocabulary and discursive practices. Secondly, it argues that both approaches lead to differing understandings of the role of “truth” and “falsity” in moral discourse. On the one hand, Wittgenstein’s remarks on ethics demonstrate a dismissive attitude towards the notions of truth and falsity in moral discourse. On the other hand, Brandom seems to be committed to a weak version of moral cognitivism: he takes assertions (which express beliefs, i.e. doxastic commitments) as the fundamental linguistic activity in the game of giving and asking for reasons and provides an anaphoric theory of truth to account for “truth” and “falsity” in our discourse. Additionally, it analyses how these differences bear on the Frege–Geach problem. (shrink)

From a Wittgensteinian point of view, my goal is to argue against the idea that teaching critical thinking should have as one of its aims the possibility of changing or adapting our deeply held beliefs. As pointed out by the Austrian philosopher in On Certainty, we have a world-picture which is neither true nor false, but above all, ‘it is the substratum of all my enquiring and asserting’. Besides that, in his remarks on Frazer’s Golden Bough, Wittgenstein insists on the (...) idea that different communities have their own rituals that express ways of acting, which become crystallized in their customs and institutions, similar to the magical rituals described by Frazer. The degree of similarity among them is greater than we suspect, and what interested Wittgenstein was to understand how we see things by looking for the links between the various ritualistic events. Based on these remarks, I argue that, if our deeply held beliefs are a source of necessity, instead of aiming to change/adapt them, teaching critical thinking should—by showing the links between diverse cultures—essentially avoid employing them in a dogmatic way, since our own deeply held beliefs could have been different ones. (shrink)

My aim in this paper is twofold: to establish that Kierkegaard's so‐called theory of the leap strongly anticipates a line of argument that is central to Wittgenstein's so‐called rule‐following considerations; and to begin to show how Kierkegaard's work has fruitful contributions of its own to make to on‐going discussions about rules and rule‐following. The paper focuses throughout on the question of how, if at all, human rule‐following can be distinguished from behaviour that is merely mechanical or instinctual. I identify a (...) central line of argument in Wittgenstein that problematizes this question by establishing the basis our ability to follow rules in our spontaneous responses. I argue that Kierkegaard not only strongly anticipates this line of argument but also offers a distinctive story about what, at bottom, makes the difference between human rule‐following and behaviour that is merely mechanical or instinctual. In a word, on Kierkegaard's story, what makes the difference is: anxiety. (shrink)

In this article, I show and discuss the relevance of Wittgenstein's arguments as to the spatial structure of sight to recent issues in the philosophy of mind. The first, bearing upon the dimensionality of the manifolds at play in depiction, plays a critical role in Clark's attempt to provide an independent account ofqualiaand of their differentiative properties. The second, pertaining to the properly spatial structure formed by the data of sight, is explicitly appealed to in the debate on the realistic (...) character of any genuinely spatial scheme. I argue that if Wittgenstein rightly assumes that the simultaneous presence of sensible places in vision is a key condition for objectivity, he fails nevertheless to warrant the allegedly realistic character of the scheme employed in his own search for a phenomenological description of the visual field. (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)