According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of arithmetic. On (...) this account, the intended models of arithmetic are the notation systems with recursive operations on them satisfying the Peano axioms. [A]m Anfang […] ist das Zeichen. (shrink)

W. Tait, The provenance of pure reason. Essays in the philosophy of mathematics and its history. New York: Oxford University Press, 2005. ix + 332 pp. £36.50. ISBN 0-19-514192-X. Reviewed by J. W....

This paper explains three ways to develop a conceptual role view of meaning in metaethics. First, it suggests that there’s a way to combine inspiration from noncognitivism with a particular form of the conceptual role view to form a noncognitivist view with distinctive advantages over other noncognitivist views. Second, it suggests that there’s also a way to combine a strong commitment to cognitivism with a different form of the conceptual role view to form a version of cognitivism with distinctive advantages (...) over other cognitivist views. Finally, it suggests that there's another way to think of the conceptual role view in metaethics is as opening up the space for a third way, beyond cognitivism and noncognitivism. (shrink)

En este artículo me propongo revisar en qué medida cabría atribuir a Wittgenstein la responsabilidad de haber propiciado un «giro retórico» con sus inquisiciones filosóficas, correlativo al giro más general, en el mismo sentido, que, según recientemente se ha venido reconociendo, habría sufrido nuestra cultura en los últimos tiempos. Dado que cabe leer la obra de Wittgenstein como si una de sus más pujantes preocupaciones consistiese en dilucidar qué debemos entender hoy por racionalidad, el mentado «giro retórico», de haberse cumplido (...) en él, podría leerse como algo que atañe cardinalmente a tal cuestión. Explicaremos primeramente, pues, en qué consiste efectuar un giro retórico en la filosofía acerca de la racionalidad; para trasladarnos posteriormente a sopesar la presencia de tal giro en Wittgenstein (y de Wittgenstein en tal giro). (shrink)

The concept of a rule that primarily interests Wittgenstein is one that is central to our understanding of 'what is possible before all new discoveries and inventions'. Wittgenstein's investigations of the concept of a rule run 'criss‐cross in every direction'. As Wittgenstein points out, 'any interpretation still hangs in the air along with what it interprets, and cannot give it any support'. Like our inner mental picture of a cube, what we think of as an interpretation of a rule doesn't (...) by itself predetermine the steps that accord with the rule it supposedly interprets. In his great work, Philosophical Investigations, Wittgenstein aims both to uncover the sources of these difficulties and to show his readers how to overcome them. In particular, he aims to expose the emptiness of tempting philosophical explanations of the notion of grounds for correct continuation of a rule. (shrink)

Explores the central role in Wittgenstein's later work of his opposition to a 'mechanistic' conception of understanding. Offers a diagnosis of Kripke's skeptical paradox on this basis.

In his well-known essay on Wittgenstein, Saul Kripke maintains that dispositional analyses of meaning cannot work mainly because the concept of disposition is descriptive, whereas that of meaning is normative. Unfortunately, neither Kripke nor his followers have ever spelled out this “argument from normativity” in full detail. As a result, the argument does not have good press. This paper offers an explicit version of the argument. In particular, (1) I try to explain what the claim that meaning is normative amounts (...) to, (2) I try to clarify what supports it, and (3) I sketch a valid version of the argument. (shrink)

El texto que se presenta aquí es la segunda parte de la traducción de New Theory of Universalsy se corresponde con las últimas secciones del artículo original. En el anterior número de Ideas y Valores (157 de abril de 2015) se publicó la primera parte, que corresponde a la introducción y las dos primeras secciones del original.

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

Over the past century or so, questions concerning the word ‘meaning’ have been understandably prominent in the field of the philosophy of language. There is, however, a historical aspect to the debate that is of especial interest to literary critics – the fact that verbs and expressions of meaning have been applied to different kinds of things in a number of languages spanning the western literary tradition. I shall introduce the topic by focussing on the Latin expressionsibi uelleand on how (...) Roman authors exploited its ambiguities for the purposes of humour (§§ I and II). I shall then move on to a discussion of a later Latin phrase familiar from the pages of the Virgilian commentator Servius,hoc uult dicere, and argue that the assumptions we have about expressions of meaning may lead us to adopt a particular interpretation of it (§§ III and IV). In the final part of the paper (§§ V, VI and VII) I shall proceed to a discussion of why it is important for modern literary critics to pay attention to how they use verbs such as ‘to mean’: I argue that the different functions of the verb facilitate a personification of the text that allows us to equivocate about the role of the author. (shrink)

What is understanding? My goal in this paper is to lay out a new approach to this question and clarify how that approach deals with certain issues. The claim is that understanding is a matter of compressing information about the understood so that it can be mentally useful. On this account, understanding amounts to having a representational kernel and the ability to use it to generate the information one needs regarding the target phenomenon. I argue that this ambitious new account (...) can accommodate much of the data that has motivated theories of understanding in philosophy of science, and can also be generally applicable in epistemology and daily life as well. (shrink)

The philosophical literature on reasoning is dominated by the assumption that reasoning is essentially a matter of following rules. This paper challenges this view, by arguing that it misrepresents the nature of reasoning as a personal level activity. Reasoning must reflect the reasoner’s take on her evidence. The rule-following model seems ill-suited to accommodate this fact. Accordingly, this paper suggests replacing the rule-following model with a different, semantic approach to reasoning.

What exactly is reasoning? While debate on this question is ongoing, most philosophers seem to agree on at least the following: reasoning is a mental process operating on contents, which consists in adopting or revising some of your attitudes in light of others. In this paper, I argue that this characterisation is mistaken: there is no single mental phenomenon that satisfies both of these conditions. Instead, I characterise two distinct mental phenomena, which I call ‘deducing’, on the one hand, and (...) ‘reasoning’ or ‘inference’ on the other, to play each of these roles. Recognising this division of labour is essential to developing a better understanding of our rational economy. (shrink)

ArgumentThis paper builds on a neglected philosophical idea,Evidenz. Max Weber used it in his discussion ofVerstehen, as the goal of understanding either action or such things as logic. It was formulated differently by Franz Brentano, but with a novel twist: thatanyonewho understood something would see the thing to be understood as self-evident, not something dependent on inference, argument, or reasoning. The only way one could take something as evident in this sense is by being able to treat other people as (...) having the same responses – by empathy with them, in the weak sense of following their thought. Brentano's philosophical claim is that without some stopping point at what is self-evident, justifications fall into infinite regress. This is radically opposed to much of conventional philosophy. The usual solutions to the regress problem rely on problematic claims about the supposed hidden transcendental structure behind reasoning. In contrast, empathy is a genuine natural phenomenon and a better explanation for the actual phenomenon of making sense of the reasoning of others. What is evident to all who are capable of understanding is an empirically-defined subset of this class. (shrink)

In this reply, I raise some questions about the account of "normativity" given by Joseph Rouse. I discuss the historical form of disputes over normativity in such thinkers as Kelsen and show that the standard issue with these accounts is over the question of whether there is anything added to the normal stream of explanation by the problem of normativity. I suggest that Rouse’s attempt to avoid the issues that arise with substantive explanatory theories of practices of the kind criticized (...) in The Social Theory of Practices leads to a result that is uninformative, and the strategy raises the question of whether there is anything there to explain and thus whether there is any necessity to appeal to the kind of anomalous explanations the normativist offers. Key Words: Kelsen • normativity • Mauss • naturalism • practices. (shrink)

The reviewers Rapaport, Stephanou, Angius, Primiero, and Bringsjord of Turner cover a broad range of topics in the philosophy of computer science. They either challenge the positions outlined in Turner or offer a more refined analysis. This article is a response to their challenges.

Historians must be sensitive to the alienness of the past. Insofar as they are concerned with their actors’ reasoning, they must (through open-minded empirical investigation) find out how their actors thought, and not assume that they thought like us. This is familiar historiographical advice, but pushed too far it can be brought to conflict with rather weak assumptions about what historians must presuppose if they are to interpret their actors at all. The present paper sketches those assumptions, and argues that (...) the influential ‘Strong Program’ in the Sociology of Scientific Knowledge (SSK) falls foul of them. We do not argue from the correctness of the assumptions to the falsity of SSK. Rather, we note the incompatibility, and then show how SSK theorists’ tendency to take interpretation for granted blinds them—and perhaps their readers—to the existence of the conflict. (shrink)

This article takes up Winch’s exploration of a certain dialectic in philosophical accounts of social inquiry, the poles of which I refer to as the under-laborer and over-laborer conceptions of philosophy. I argue that these conceptions, shown in Risjord and Reed, respectively, are caught in a dialectic of treating philosophy’s roles as either modestly clarifying or broadly determining the claims of social science. A third conception of philosophy, the therapeutic conception, is exemplified by Read et al.’s “New Wittgensteinian” interpretation of (...) Winch’s work as a way out of the dialectic. Discussing the strengths and weaknesses of the latter, I conclude that a stronger development of the therapeutic approach is needed to move past the dialectic. (shrink)

Dewey’s social ontology could be characterized as a habit ontology, an ontology of habit qua second nature that offers us an account of intentionality, social statuses, institutions, and norms in terms of habituations. Such an account offers us a promising alternative to contemporary intentionalist and deontic approaches to social ontology such as Searle’s. Furthermore, it could be the basis of a social ontology better suited to explain both the maintenance and the transformation of social reality. In the first part I (...) will characterize Dewey’s model as a social ontology based on the notion of habit, and present it as an alternative to intentionalist approaches to social reality. In the second part I will argue that habit ontology offers us an account of social norms that is based on a peculiar understanding of the notion of ‘status’, and represents an alternative to deontic accounts. In the third part I will claim that Dewey’s notion of “public” offers us a dynamic understanding of social institutions and a ‘reactive’ notion of collective intentionality as an achievement rather than as a presupposition of social practices. In the final section I will summarize some advantages of the Deweyan over the Searlean social ontology concerning our understanding of acceptance, maintenance and transformation of statuses, and of the role played by the ‘background’. (shrink)

Of course, I do not mean by the title of this paper to deny the existence of something called.

The paper attempts to construct a theoretical account of what melancholy—in a psychoanalytical and cultural sense—may mean for jurisprudence. It argues that the map of relations and displacements between the object and the subject that is associated with melancholy in different psychoanalytical approaches can be fruitfully adopted for understanding of normativity. Based on a thorough re-reading of Freud’s Trauer und Melancholie, it suggests that there is an irremovable component of melancholy contained in the primordial act of separation of normativity from (...) non-normative reality. This interpretation is confronted with Kelsen’s Theory of Pure Law in order to analyse in which respect the momentum of self-sufficiency within normativity entails structures of melancholy. Kelsen’s concept of ‘effectiveness’ is proposed as a key link which explains how melancholic withdrawal allows the law to interact with reality. Then the paper discusses Agamben’s theory of applicability and of the state of exception to demonstrate the law’s melancholic trap. Finally, the paper draws on Lacanian and post-Lacanian approaches to melancholy in order to investigate how melancholic momentum is inherent in the very structure of the law’s validity. (shrink)

The debate over physicalism in philosophy of mind can be seen as concerning an inconsistent tetrad of theses: (1) if physicalism is true, a priori physicalism is true; (2) a priori physicalism is false; (3) if physicalism is false, epiphenomenalism is true; (4) epiphenomenalism is false. This paper argues that one may resolve the debate by distinguishing two conceptions of the physical: on the theory‐based conception, it is plausible that (2) is true and (3) is false; on the object‐based conception, (...) it is plausible that (3) is true and (2) is false. the paper also defends and explores the version of physicalism that results from this strategy. (shrink)

Wittgenstein constantly invokes teaching, training and learning in his later work. It is therefore interesting to consider what role these notions play for him there. I argue that their use is central to Wittgenstein’s attempt to refute cognitivist assumptions, and to show how normative practices can be understood without the threat of circularity, grounded not in a kind of seeing, but in doing, and the natural reactions of an organism. This can generate a worry that Wittgenstein’s position is quietist and (...) anti-critical: critique, as a challenge to the taken-for-granted grammar of our language game, is technically meaningless. I argue that Wittgenstein does not rule out critique. His own practice demonstrates that critique is possible, but takes place within a language game, and its status as critique is always subject to challenge in the agora of a discourse. (shrink)

I hope to clarify and explicate an account of how a creature comes to be brought into the space of reasons – that is, comes to take its place as a rational agent in social practices. My ultimate interest, however, is with a tension apparently generated by the emphasis on training coupled with this attack on cognitivism. If one’s coming to maturity depends on one being embedded in a practice, so that one comes to adopt, with ‘comfortable certainty’, the common (...) ground of that practice’s language games, then there seems to be no position from which to frame a critique of a practice. (shrink)

Rule following is often made an unnecessary mystery in the philosophy of social science. One form of mystification is the issue of 'rule finitism', which raises the puzzle as to how a learner can possibly extend the rule to applications beyond those examples which have been given as instruction in the rule. Despite the claim that this problem originated in the work of Wittgenstein, it is clear that his philosophical method is designed to evaporate, not perpetuate, such problems. The supposed (...) problem of rule finitism is malformed, deriving from misconceptions about the relation between understanding a rule and making an application of it. (shrink)

This article argues that two significant implications of Wittgenstein’s writings for social thought are (1) that people are constitutively social beings and (2) that the social context of an individual life is nexuses of practice. Part one concretizes these ideas by examining the constitution of action within practices. It begins by criticizing three arguments of Winch’s that suggest that action is inherently social. It then spells out two arguments for the practice constitution of action that are extractable from Wittgenstein’s remarks. (...) Part two contrasts the conception of the social context of individual life as practices with three historically significant conceptions of such a context: totality; sui generis reality; and abstract structure. It also circumscribes that contemporary movement - practice theory - that develops the Wittgensteinian position and represents, perhaps, his most significant legacy for social thought. (shrink)

Analytic skill can contribute to a theology of the Bible and a theological hermeneutic in two ways, by refining the formulation of a doctrine of Scripture and a correlative hermeneutic, and by illuminating how problematic hermeneutical presuppositions have in some cases become part of exegetical practice. The contribution that the analytic style of reflection can make to the theological enterprise need not be vitiated by a common criticism of analytic modes of engaging with texts, namely, that they tend toward being (...) ahistorical, though the objection deserves to be considered carefully. (shrink)

ABSTRACTCarnap famously argued that there are two kinds of questions and claims concerning the existence or reality of entities: internal and external ones. We focus on Carnapian external ontological claims of the form: ‘Xs really exist’, where ‘X’ stands for some traditional metaphysical category, such as ‘substance’, ‘fact’ or ‘structure’. While Carnap considered them as meaningless, we consider them as faultlessly meaningful. However, in line with an expressivist guise, we do not claim that they have the meaning they have in (...) virtue of representing a certain range of entities in the world or describing pieces of reality. Quite the contrary, we maintain that they are meaningful because they perform a function that is fundamentally expressive, that is, a non-descriptive function. In particular, they may imply a distinctive type of metalinguistic expressive function. Moreover, we avoid accuses of mentalism insofar as we explain the meaning of external ontological claims in terms of the practical commitments to the adoption of certain linguistic forms they express, rather than as expressing some kind of mental state. (shrink)

Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...) this, I argue that semantics can fail to deliver determinate ontological commitments and determinate answers to ontological questions, more generally. (shrink)

The main question of metasemantics, or foundational semantics, is why an expression token has the meaning (semantic value) that it in fact has. In his reading of Ludwig Wittgenstein’s later work, Saul Kripke presented a skeptical challenge that threatened to make the foundational question unanswerable. My first contention in this paper is that the skeptical challenge indeed poses an insoluble paradox, but only for a certain kind of metasemantic theory, against which the challenge effectively works as a reductio ad absurdum (...) argument. My second contention is that as a result of rejecting the theory which entails a paradoxical outcome, we will see that the foundational question essentially involves a temporal dimension. After arguing that the skeptical challenge gives us a strong reason to adopt a historical view of meaning, I shall further argue against certain authors who claim that meanings not only have histories but futures as well, or that the meaning of a word may change retroactively in time as a consequence of counterfactual change in its future use. The major aim of the paper is thus to bring together the arguably interrelated debates about the skeptical challenge and temporal externalism in philosophy of language. (shrink)

We evaluate the richness of the child’s input in semantics and its relation to the hypothesis space available to the child. Our case study is the acquisition of the universal quantifier every. We report two main findings regarding the acquisition of every on the basis of a corpus study of child-directed and child-ambient speech. Our first finding is that the input in semantics is rich enough to systematically eliminate instances of the subset problem of language acquisition: overly general hypotheses about (...) the meaning of every can violate pragmatic constraints, making such hypotheses incompatible with the child’s input. Our second finding is that the semantic input is too poor to eliminate instances of what we refer to as the superset problem, the mirror image of the subset problem. We argue that at least some overly specific hypotheses about the meaning of every are compatible with the child’s input, suggesting either that those hypotheses are not made available by UG or that non-trivial inductive biases are involved in children’s acquisition of every. (shrink)

The section we have examined is a persuasive and sustained demolition of the realist strategy of deriving an invariable concomitance between the existenthood of the world and the system of validation (a system accepted by both parties as being the regulator of epistemic activity). This leaves the Advaitin with an absence of invariable concomitance. This is where the Advaitin wants to be. On his view, the absence of this concomitant dependence of the system of validation on an ‘existent’ world points (...) to the possibility that the cognized world is not that independent world which Nyāya takes to be the determinate reality. If that world is not philosophically proven to be so independent, then there is at least aprima facie case for the Advaitic soteriological claim that it is Brahman alone which is ultimately real, even though the commonly cognized world allows of coherent epistemic activity. It is fair to say that such a view is established by the failure of the opponent to prove invariable concomitance between inquiry, validation and an independent world. It is the inability of the opposing view to prove a metaphysical claim which itself points to the nature of the Advaitic position; the position, that is, which suspends the need to make an ontic commitment to the extrinsic world as a determinate reality. Whether the critique of the Nyāya concept ofsattā takes us to the refutation of the Nyāya concept of a determinate world (and whether the Advaitic rejection ofsattā is of a piece with the concept of an ‘indeterminate’ world) is another issue, dealt with in detail by Śrī Har $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s} $$ a elsewhere in his book, but beyond the purview of this paper. (shrink)

The idea that there are features of or in our conscious experience that are, in some important sense, private has both a long history in philosophy and a large measure of intuitive attraction. Once this idea is in place, it will be very natural to assume that one can think and judge about one’s own private features. And it is then only a small step to the idea that we might communicate such thoughts and judgements about our respective private features (...) with each other. (shrink)

According to the quotational theory of meaning ascriptions, sentences like “‘Bruder means brother” are abbreviated synonymy claims, such as “‘Bruder means the same as ‘brother’”. After discussing a problem with Harman’s version of the quotational theory, I present an amended version defended by Field. Then, I address Field’s responses to two arguments against the theory that revolve around translation and the understanding of foreign expressions. Afterwards, I formulate two original arguments against both Harman’s and Field’s versions of the theory. One (...) of them targets the hyperintensionality of quotations and the other raises a problem pertaining to variant spellings of words. (shrink)

ABSTRACTThis paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit taking, we posit (...) rich inferential transitions, which are transitions that the subject is disposed to endorse. (shrink)

Karczmarczyck evalúa y critica algunas tesis centrales defendidas en mi libro Vericuetos de la filosofía de Wittgenstein en torno al lenguaje y el seguimiento de reglas, centrado en las ideas del segundo Wittgenstein. Debato aquí sobre diversos puntos examinados por Karczmarczyck. En particular: rechazo su concepción antirrealista de la intencionalidad, según la cual factores posteriores a una acción pueden determinar que dicha acción sea o no una acción deliberada; exploro otros aspectos de la contraposición realismo/antirrealismo, vinculándolos con la lectura antirrealista (...) que Kripke, Karczmarczyck y otros autores hacen de Wittgenstein; explico por qué no es circular mi solución disposicional-teleológica al enigma sobre seguir una regla. (shrink)

This essay argues that the main lesson of Lewis Carroll's Regress is that arguments are constitutively presuppositional.

Physicalism about colour is the thesis that colours are identical with response-independent, physical properties of objects. I endorse the Argument from Structure against Physicalism about colour. The argument states that Physicalism cannot accommodate certain obvious facts about colour structure: for instance, that red is a unitary colour while purple is a binary colour, and that blue resembles purple more than green. I provide a detailed formulation of the argument. According to the most popular response to the argument, the Physicalist can (...) accommodate colour structure by explaining it in terms of colour experience. I argue that this response fails. Along the way, I examine other interesting issues in the philosophy of colour and colour perception, for instance the relational structure of colour experience and the description theory of how colour names refer. (shrink)

In this paper, we would like to discuss Wittgenstein’s critique of the idea that a person’s experiences are necessarily private, and these experiences can only be expressible in a private language. Taking a clue from Wittgenstein, we intend to say that the person’s experiences though private, can also be known by others. In the following sections 243 of his Philosophical Investigations, Wittgenstein argues against the possibility of a private language about the subject’s inner experiences. He contends that by coining names/words (...) to name sensations and our inner experiences, we cannot create a private language. If we have a list of names, that cannot function as a language. We need predicate terms; we need the syntax to link the words in the form of a sentence. If we use private names and use the predicates from the language that everyone knows, then the private words will acquire public status like the terms ‘pain’ and ‘sensation.’ These terms are already part of the public language, and if private experiences like pain and sensation cannot be made public, we would not have these terms in our language at all. This is the reason why any application of words is public, and therefore, there is no possibility of a private language. Wittgenstein concentrates on the public rules that govern the correct application for the use of words. And the expressions are meaningful only when these are used according to rules of grammar; if these expressions do not follow any rules of grammar, these are simply meaningless. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a (...) variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others. (shrink)

In this essay I consider what is meant by the description ‘great’ philosophy and then offer some broadly applicable criteria by which to assess candidate thinkers or works. On the one hand are philosophers in whose case the epithet, even if contested, is not grossly misconceived or merely the product of doctrinal adherence on the part of those who apply it. On the other are those – however gifted, acute, or technically adroit – to whom its application is inappropriate because (...) their work cannot justifiably be held to rise to a level of creative-exploratory thought where the description would have any meaningful purchase. I develop this contrast with reference to Thomas Kuhn’s distinction between ‘revolutionary’ and ‘normal’ science, and also in light of J.L. Austin’s anecdotal remark – à propos Leibniz – that it was the mark of truly great thinkers to make great mistakes, or to risk falling into certain kinds of significant or consequential error. My essay goes on to put the case that great philosophy should be thought of as involving a constant readiness to venture and pursue speculative hypotheses beyond any limits typically imposed by a culture of ‘safe’, well-established, or academically sanctioned debate. At the same time – and just as crucially – it must be conceived as subject to the strictest, most demanding standards of formal assessment, i.e., with respect to basic requirements of logical rigour and conceptual precision. Focusing mainly on the work of Jacques Derrida and Alain Badiou I suggest that these criteria are more often met by philosophers in the broadly ‘continental’ rather than the mainstream ‘analytic’ line of descent. However – as should be clear – the very possibility of meeting them, and of their being jointly met by any one thinker, is itself sufficient indication that this is a false and pernicious dichotomy. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

This paper argues that autonomy is an educational ideal. Since personal autonomy is essentially a matter of the person governing herself, a plausible account of autonomy presupposes an account of u person's identity. I support a conception of autonomy which presupposes a hierarchical theory of the self, yet allows rationality a significant place in a person's identity. I defend this conception of autonomy as an educational ideal from recent criticisms by Stone (1990) and Cuypers (1992).