The task of this paper is to exhibit Wittgenstein’s method of perspicuous presentation as aiming at a distinctive kind of self-knowledge. Three influential readings of Wittgenstein’s concept of perspicuous presentation – Hacker’s, Baker’s and Sluga’s – are examined. All of them present what Wittgenstein calls the “unsurveyablity of our grammar” as a result of the “complexity” of our language. Contrary to this, a fundamental difference between matter-of-factual complexity and the unsurveyability of grammar is pointed out. What perspicuous presentations are designed (...) to deal with, isn’t, accordingly, occasioned by the complexity of our language but by an unnoticed assimilation of our own activities as speaking beings to matter-of-factual affairs. In response to this, perspicuous presentations help us to fully appropriate our activities as speakers in virtue of achieving a transparent understanding of the use of “our words”. It thus provides us with a distinctive kind of grammatical self-knowledge. (shrink)

The paper submits a criticism of the standard formulation of Wittgenstein’s rule-following paradox. According to the standard formulation, influenced by Kripke, the paradox invites us to consider what mental or behavioral items could constitute meaning. The author proposes instead an enactivist understanding of the paradox. On this account there is no essential gap between mental items and behavioral patterns such that the paradox enforces a choice between meaning being constituted either internally ‘in mind,’ or externally ‘in behavior.’ The paper begins (...) with an introduction to the paradox and then presents arguments against standard solutions. It ends with the enactivist proposal, admitting that although much more needs to be said before it can be established as a full-fledged alternative, it nonetheless holds some promise both for revising our understanding of the paradox and for the formulation of a novel solution. (shrink)

Walter Dubislav (1895–1937) was a leading member of the Berlin Group for scientific philosophy. This “sister group” of the more famous Vienna Circle emerged around Hans Reichenbach’s seminars at the University of Berlin in 1927 and 1928. Dubislav was to collaborate with Reichenbach, an association that eventuated in their conjointly conducting university colloquia. Dubislav produced original work in philosophy of mathematics, logic, and science, consequently following David Hilbert’s axiomatic method. This brought him to defend formalism in these disciplines as well (...) as to explore the problems of substantiating (Begründung) human knowledge. Dubislav also developed elements of general philosophy of science. Sadly, the political changes in Germany in 1933 proved ruinous to Dubislav. He published scarcely anything after Hitler came to power and in 1937 committed suicide under tragic circumstances. The intent here is to pass in review Dubislav’s philosophy of logic, mathematics, and science and so to shed light on some seminal yet hitherto largely neglected currents in the history of philosophy of science. (shrink)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (shrink)

Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. It will be (...) shown that strict finitism entails none of these assumptions. Hence, the argument does not prove that the view is internally incoherent, and consequently, Dummett fails to undermine the Wittgensteinian conception of meaning. (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)

This paper aims to distinguish Wittgenstein’s concept of ‘form of life’ from other concepts or expressions that have been confused or conflated with it, such as ‘language-game’, ‘certainty’, ‘patterns of life’, ‘ways of living’ and ‘facts of living’. Competing interpretations of Wittgenstein’s ‘form of life’ are reviewed, and it is concluded that Wittgenstein intended both a singular and a plural use of the concept; with, where the human is concerned, a single human form of life characterized by innumerable forms of (...) human life. (shrink)

The outcomes of educational assessments undoubtedly have real implications for students, teachers, schools and education in the widest sense. Assessment results are, for example, used to award qualifications that determine future educational or vocational pathways of students. The results obtained by students in assessments are also used to gauge individual teacher quality, to hold schools to account for the standards achieved by their students, and to compare international education systems. Given the current high-stakes nature of educational assessment, it is imperative (...) that the measurement practices involved have stable philosophical foundations. However, this article casts doubt on the theoretical underpinnings of contemporary educational measurement models. Aspects of Wittgenstein’s later philosophy and Bohr’s philosophy of quantum theory are used to argue that a quantum theoretical rather than a Newtonian model is appropriate for educational measurement, and the associated implications for the concept of validity are elucidated. Whilst it is acknowledged that the transition to a quantum theoretical framework would not lead to the demise of educational assessment, it is argued that, where practical, current high-stakes assessments should be reformed to become as ‘low-stakes’ as possible. This article also undermines some of the pro high-stakes testing rhetoric that has a tendency to afflict education. (shrink)

In this paper, I will investigate Wittgenstein’s idea about the context-sensitivity of utterance. It is the idea that there is a big gap between understanding a sentence in the sense of knowing the idioms and discerning the grammar in it, and what is said by using it in a particular context. Although context-sensitivity in this moderate sense is a familiar idea in Wittgensteinian scholarship, it has mainly been studied as an idea in “Wittgenstein’s philosophy of language.” However, Wittgenstein’s interest in (...) language is always connected with his interest in the treatment of philosophical problems. Therefore, what is lacking in those preceding studies is the study of the relation between Wittgenstein’s engagement with the idea of context-sensitivity and his philosophical therapy. Therefore, I shall investigate that relation and show that Wittgenstein’s philosophical method cannot be intelligible without taking context-sensitivity into consideration and Wittgenstein’s focus on context is deeply connected with his method for treating philosophers’ “pictures.” Below, I will examine recent debates on grammar, and argue that the standard interpretation is untenable once proper consideration is given to context-sensitivity. Next, I will argue that context-sensitivity is important because it gives us a good grasp of the process of a philosopher’s being caught in a picture by citing the discussion about mental process and about the Augustinian picture and rule-following in Philosophical Investigations. Finally, I will talk about the significance of my interpretation for contemporary arguments about philosophical methods. (shrink)

According to the dominant view, the later Wittgenstein identified the meaning of an expression with its use in the language and vehemently rejected any kind of mentalism or intentionalism about linguistic meaning. I argue that the dominant view is wrong. The textual evidence, which has either been misunderstood or overlooked, indicates that at least since the Blue Book Wittgenstein thought speakers' intentions determine the contents of linguistic utterances. His remarks on use are only intended to emphasize the heterogeneity of natural (...) language. Taking into account remarks written after he finished the Investigations, I show how Wittgenstein anticipated the basic tenets of Gricean intention-based semantics. These are, in particular, the distinction between ‘natural’ and ‘non-natural’ meaning and the distinction between what a speaker means by an utterance and what the expression uttered means in the speaker’s natural language. Importantly, Wittgenstein also believed that only the meaning of the speaker determined the content of ambiguous expressions, such as ‘bank’, on a particular occasion of utterance. (shrink)

Inducing aspect-experiences – the sudden seeing of something anew, as when a face suddenly strikes us as familiar – can be used as a philosophical method. In seeing aspects, I argue, we let ourselves experience what it would be like to conceptualize something in a particular way, apart from any conceptual routine. We can use that experience to examine our ways of conceptualizing things, and re-evaluate the ways we make sense of them. I claim that we are not always passive (...) with regard to these experiences, and explain how we can actively induce them. I distinguish this method from other standard Wittgensteinian philosophical methods. (shrink)

This volume consists of the invited papers presented at the 23rd International Wittgenstein Conference held in Kirchberg, Austria in August 2000. Among the topics treated are: truth, psychologism, science, the nature of rational discourse, practical reason, contextualism, vagueness, types of rationality, the rationality of religious belief, and Wittgenstein. Questions addressed include: Is rationality tied to special sorts of contexts? ls rationality tied to language? Is scientific rationality the only kind of rationality? Is there something like a Western rationality? and: Could (...) we genetically engineer human beings to be less wicked? (shrink)

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)

In this essay, the tension that Benacerraf identifies for theories of mathematical truth is used as the vehicle for arguing against a particular desideratum for semantic theories. More specifically, I place in question the desideratum that a semantic theory, provided for some area of discourse, should run in parallel with the semantic theory holding for the rest of the language. The importance of this desideratum is also made clear by means of tracing out the subtle implications of its rejection.

Peter Ludlow shows how word meanings are much more dynamic than we might have supposed, and explores how they are modulated even during everyday conversation. The resulting view is radical, and has far-reaching consequences for our political and legal discourse, and for enduring puzzles in the foundations of semantics, epistemology, and logic.

outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.

This multifaceted essay emerges from a host of sources within diverse academic settings. Its central thesis is guided by physicist John A. Wheeler's thoughts on the quantum enigma. Wheeler concludes, following Niels Bohr, that we are co-participants within the universal self-organizing process. This notion merges with concepts from Peirce's process philosophy, Eastern thought, issues of topology, and border theory in cultural studies and social science, while surrounding itself with such key terms as complementarity, interdependence, interrelatedness, vagueness, generality, incompleteness, inconsistency, and (...) mestizaje. Ultimately, a sense of semiosic process pervades in light of combined homogenous and hetergenous tendencies. (shrink)

Drawing heavily on Wittgenstein, Winch’s The Idea of a Social Science advanced a forceful and still valuable critique of positivist/empiricist conceptions of social science. In its more self-confident assertions concerning the nature of philosophy and society, however, Winch failed to recognize Wittgenstein’s acknowledgement of and appreciation for the indeterminacy and unsettled character of social and moral life.

In his Wittgenstein on Rules and Private Language , Saul Kripke presents his influential reading of Wittgenstein’s later writings on language. One of the largely unexplored features of that reading is that Kripke makes a small number of suggestive remarks concerning the possible threat that Wittgenstein’s arguments pose for Chomsky’s linguistic project. In this paper, we attempt to characterise the relevance of Wittgenstein’s later work on meaning and rule-following for transformational linguistics, and in particular to identify the potentially negative impact (...) it has on that project. Although we use Kripke’s remarks to articulate some of the pertinent issues, we return to Wittgenstein’s later writings to address them. We argue that Wittgenstein’s main target in the relevant sections of the Philosophical Investigations is the notion of ‘logical compulsion’, which involves assuming that there is more to applying a word or rule than how we are naturally or “psychologically” compelled to apply. We characterise two of the main lines of argument in the Investigations in terms of the rejection of logical compulsion. We thus propose to address the relevance of Wittgenstein’s writings for Chomsky by considering whether Chomsky’s linguistics presupposes the targeted notion of logical compulsion. We argue that Chomsky’s conception of linguistic competence in terms of successive states of the “language faculty” (containing the principles of universal grammar) does presuppose this problematic notion. Chomsky responded to Kripke by devoting a chapter of his Knowledge of Language to defending this conception of linguistic competence against the Wittgensteinian arguments. We evaluate his response and argue that he has misidentified the threat to his linguistic project as consisting in the attack on its ‘individual psychology’ standpoint, rather than its commitment to logical compulsion. We conclude by arguing that Chomsky’s attempts at defending his individualist or non-communitarian standpoint are undermined by his inability to give a decisive response to Wittgenstein’s attack on logical compulsion. (shrink)

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.

The collection Virtual Mathematics: the logic of difference brings together a range of new philosophical engagements with mathematics, using the work of French philosopher Gilles Deleuze as its focus. Deleuze’s engagements with mathematics rely upon the construction of alternative lineages in the history of mathematics in order to reconfigure particular philosophical problems and to develop new concepts. These alternative conceptual histories also challenge some of the self-imposed limits of the discipline of mathematics, and suggest the possibility of forging new connections (...) between philosophy and more recent developments in mathematics. This component of Deleuze’s work has, to date, been rather neglected by commentators working in the field of Deleuze studies. One of the aims of this collection is to address this critical deficit by providing a philosophical presentation of Deleuze’s relation to mathematics; one that is adequate to his project of constructing a philosophy of difference and to the exploration of some of its applications. This project developed as a result of encounters with an increasing number of researchers who have been working on the mathematical aspects of Deleuze’s work and the key role that these play in his philosophy. By bringing this work together for the first time, this collection makes an important contribution to the emerging body of work that endeavours to explore the broad range of Deleuze’s philosophy. (shrink)

I articulate Charles S. Peirce’s philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce’s philosophy of mathematical education primarily aims at fostering the development of the students’ semeiotic abilities of imagination, concentration, and generalization required for conducting mathematical inquiry by way of experimentation upon diagrams. This involves an emphasis on the relation between theory and practice and (...) between mathematics and other fields including the arts and sciences. For achieving its goals, the article is divided in three sections. First, I expound Peirce’s philosophical account of mathematical reasoning. Second, I illustrate this account by way of a geometrical example, placing special emphasis on its relation to mathematical education. Finally, I put forth some Peircean philosophical principles for mathematical education. (shrink)

Institutions worldwide respond to the need to recognise the value of educating children and young people to handle or solve conflicts in communication. But how do they or we know that an event is correctly interpreted as a conflict? How can people analyse the quality of deliberation when handling or solving conflicts in communication in education? I discuss these questions and argue that the notion of conflict cannot be defined only in terms of incompatibility, clash, opposition and/or disagreement; it also (...) has to encompass negativity in the approach to the other. I also argue that the quality of deliberation can be analysed through a deliberative pedagogical approach, which takes into account structural features of deliberation and required dispositions of the participants, and that our knowledge of conflicts emerges holistically and is interpersonal and objective. I begin by giving an account of some institutional responses to conflicts. Then I discuss the notion of conflict and define it, inter alia, in terms of incompatibility, disagreement and negativity. Finally, I discuss ideas for analysing the quality of deliberation in communication when handling or solving conflicts in education. (shrink)

The following inquiry pursues two interlinked aims. The first is to understand Wittgenstein's idea of non-foundational certainty in the context of a reading of On Certainty that emphasizes its Pyrrhonian elements. The second is to read Wittgenstein's remarks on idealism/radical skepticism in On Certainty in parallel with the discussion of rule-following in Philosophical Investigations in order to demonstrate an underlying similarity of philosophical concerns and methods. I argue that for the later Wittgenstein, what is held certain in a given context (...) of inquiry or action is a locally transcendental condition of the inquiry or action in question. In On Certainty, Wittgenstein's analysis of the difference between knowledge and certainty forms the basis of his critique of both Moore's "Proof" and radical skepticism. This critique takes the shape of rejection of a presupposition shared by both parties, and utilizes what I identify as a Pyrrhonian-style argument against opposed dogmatic views. Wittgenstein's method in this text involves describing epistemic language-games. I demonstrate that this is consistent with the rejection of epistemological theorizing, arguing that a Wittgensteinian "picture" is not a theory, but an impressionistic description that accomplishes two things: (i) throwing into relief problems with dogmatic theories and their presuppositions, and (ii) describing the provenance of linguistic and epistemic practices in terms of norms grounded in convention. Convention, in turn, is not arbitrary, but grounded in the biological and social natures of human beings--in what Wittgenstein calls forms of life. Thus there is a kind of naturalism in the work of the later Wittgenstein. It is a naturalism that comes neatly dovetailed with Pyrrhonism--a combination of strategies traceable to Hume's work in the Treatise. I read Hume as someone who develops the Pyrrhonian method to include philosophy done "in a careless manner," and argue that Wittgenstein adopts a similar method in his later works. Finally, I explain the deference to convention in the work of both Hume and Wittgenstein by reference to a passage in Sextus' Outlines, on which I provide a gloss in the final chapter of this work. (shrink)

Abstract This paper offers an appraisal of Phillip Pettit's approach to the problem how a merely finite set of examples can serve to represent a determinate rule, given that indefinitely many rules can be extrapolated from any such set. I argue that Pettit's so-called ethnocentric theory of rule-following fails to deliver the solution to this problem he sets out to provide. More constructively, I consider what further provisions are needed in order to advance Pettit's general approach to the problem. I (...) conclude that what is needed is an account that, whilst it affirms the view that agents' responses are constitutively involved in the exemplification of rules, does not allow such responses the pride of place they have in Pettit's theory. (shrink)

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

The later Wittgenstein’s perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein’s perspective on (...) mathematical language may appeal also to those who are not friends of or experts on Wittgenstein’s later philosophy of mathematics. (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)

The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed (...) in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if φ is true, then there exists a proof of φ Building on the work of Artemov (Bull Symb Log 7(1): 1-36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence. (shrink)

Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a (...) natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs. (shrink)

The specific characteristics of mathematical argumentation all depend on the centrality that writing has in the practice of mathematics, but blindness to this fact is near universal. What follows concerns just one of those characteristics, justification by proof. There is a prevalent view that long proofs pose a problem for the thesis that mathematical knowledge is justified by proof. I argue that there is no such problem: in fact, virtually all the justifications of mathematical knowledge are ‘long proofs’, but because (...) these real justifications are distributed in the written archive of mathematics, proofs remain surveyable, hence good. (shrink)

Los estudios sociales de la ciencia y, en particular, la sociología del conocimiento científico, han criticado las filosofías de la ciencia por fundarse en epistemologías centradas en el individuo como sujeto de conocimiento, en detrimento de análisis que den cuenta de las comunidades científicas; una explicación del conocimiento científico centrada en el individuo es incapaz de dar cuenta de las tradiciones y actual estado de la ciencia. Este artículo sostiene, sin embargo, que la SSK no diluye el sujeto en la (...) comunidad científica sino que, por el contrario, permite definirlo en su interacción con otros, en la interpretación y organización del conocimiento de la naturaleza. Esto se hace recurriendo a la noción de identidad del sujeto en tanto practicante de la ciencia. (shrink)

While Wittgenstein wrote unconventionally and denied that he was advancing philosophical theses, most of his interpreters have attributed conventional philosophical theses to him. But the best recent interpretations have taken the form of his writing and his distinctive way of doing philosophy seriously. The 1980s have also seen the emergence of a body of work on Wittgenstein that makes extensive use of the unpublished Wittgenstein papers. This work on Wittgenstein's method and his way of writing are the main themes of (...) this literature review.Section 1 surveys Wittgenstein's conception of philosophical method and its reception. Section 2 is a review of recent work on rule-following and the methodological issues it raises. Section 3 concerns research on the WittgensteinNachlass and its implications for the interpretation of his philosophy. (shrink)

In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skolem's primitive recursive arithmetic and Goodstein's equational calculus, Wittgenstein represented generality by the use of free (...) variables. This has the effect that negation of unbounded universal and existential propositions cannot be expressed. This is claimed in the second section to be the basis for Wittgenstein's criticism of the universal validity of the law of excluded middle. In the last section, there is a brief discussion of Wittgenstein's remarks on real numbers. These show a preference, in line with finitism, for a recursive version of the continuum. (shrink)

This is a critical discussion of Part III of Peter Railton's recent book Facts, Values, and Norms: Essays Toward a Morality of Consequence (Cambridge University Press, 2003).

This paper discusses the coverage of ordinary language philosophy in Scott Soames' Philosophical Analysis in the Twentieth Century. After praising the book's virtues, I raise three points where I dissent from Soames' take on the history. First, I suggest that there is more to ordinary language philosophy than the rather implausible version of it that Soames sees to have been destroyed by Grice. Second, I argue that confusions between analyticity, necessity and priority are less important to the ordinary language period (...) than Soames takes them to be. Finally, I claim that Soames' criticisms of Ryle turn in part on attributing reductionist positions to Ryle that Ryle did not hold. (shrink)

In this article, extracted from his book Exploring Meinong's Jungle and Beyond, Sylvan argues that, contrary to widespread opinion, mathematics is not an extensional discipline and cannot be extensionalized without considerable damage. He argues that some of the insights of Meinong's theory of objects, and its modern development, item theory, should be applied to mathematics and that mathematical objects and structures should be treated as mind-independent, non-existent objects.

Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the contributions of Hartry Field and Eugene Wigner. Finally, I argue (...) that there are epistemological problems concerning the applicability of mathematics that nobody in the philosophical community has yet confronted, though the problems are well known to physicists. (shrink)

This paper presents an 'internal' criticism of Winch's seminal 'Understanding a Primitive Society'. It distinguishes between two contrasting approaches to critical social understanding: (1) the metaphysical approach, central to the whole tradition of critical philosophy and critical social theory from Kant, through Marx to the Frankfurt School and contemporary theorists such as Habermas and Searle; (2) the descriptive approach, advocated by Winch, and which derives from Wittgenstein's critique of philosophical theory. It is argued, against a long tradition of 'critical theory' (...) depicting Wittgenstein's philosophy as irredeemably 'conservative', that the descriptive approach is perfectly apt for generating a critical understanding of central Western institutions. Rather than seeking to provide an explanatory theory through which to discern what allegedly is imperceptible to theoretically unaided perception (i.e. the metaphysical approach), the descriptive approach aims for a 'perspicuous presentation' of our everyday practices and institutions in such a way as to see their 'irrational' and 'alienating' dimensions. Winch's basic position in 'Understanding a Primitive Society' is endorsed, but it is argued that ultimately he fails in his descriptive intent. In place of the Christian prayer analogy that Winch invokes in order to make sense of Zande witchcraft, it is proposed that Western commodity production and exchange provide a more appropriate, instructive, and critical comparison. (shrink)

The paper undertakes to characterize Hao Wang's style, convictions, and method as a philosopher, centering on his most important philosophical work From Mathematics to Philosophy, 1974. The descriptive character of Wang's characteristic method is emphasized. Some specific achievements are discussed: his analyses of the concept of set, his discussion, in connection with setting forth Gödel's views, of minds and machines, and his concept of ‘analytic empiricism’ used to criticize Carnap and Quine. Wang's work as interpreter of Gödel's thought and the (...) importance of his writings as a source are also discussed. (shrink)

Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. (...) This paper explains the main complications involved and answers the main objections advanced in Batitsky's paper in this issue. (shrink)