In virtue of what does a sign have meaning? This is the question raised by Wittgenstein's rule-following considerations. Semantic dispositionalism is a (type of) theory that purports to answer this question. The present paper argues that semantic dispositionalism faces a heretofore unnoticed problem, one that ultimately comes down to its reliance on unanalyzed notions of repeated types of signs. In the context of responding to the rule-following paradox—and offering a putative solution to it—this amounts to simply assuming a solution (...) to the problem in one domain and using it to solve the same problem in another. Given, moreover, the level at which the rule-following paradox undercuts dispositionalism—the level of the notion of a sign's repetition—the objections made to the view also rule out causal/informational theories of meaning as well as communitarian/assertion-theoretic ones as potential solutions to the rule-following paradox. (shrink)

In §201 of Philosophical Investigations, Ludwig Wittgenstein puts forward his famous "rule-following paradox". The paradox is how can one follow in accord with a rule - the applications of which are potentially infinite - when the instances from which one learns the rule and the instances in which one displays that one has learned the rule are only finite? How can one be certain of rule-following at all? In Wittgenstein: On Rules and Private Language, Saul Kripke concedes the (...) skeptical position that there are no facts that we follow a rule but that there are still conditions under which we are warranted in asserting of others that they are following a rule. In this paper, I explain why Kripke's solution to the rule-following paradox fails. I then offer an alternative. (shrink)

This article is devoted to thirtieth anniversary of the first publication in 1982 Saul Kripke's book "Wittgenstein on rules and private language". Radical skeptical interpretation of the work 'late' Ludwig Wittgenstein proposed by Saul Kripke in this book is considered one of the most famous "puzzle" of modern philosophy of language, which has become a source of much debate and discussion on the nature of the linguistic sign and its meaning. This article examines some of the consequences of a radical (...) version of skeptical 'rule-following' paradox by Saul Kripke, which remain in force and effect for finite functions and limited linguistic registers 'Ad finitum'. Thereby questioned the widely held view among analytic philosophers that the skeptical core for Saul Kripke's 'rule-following' paradox is argument 'Ad infinitum' (an inherent source of skepticism for our intention to follow the rule is concluded in itself situation of mastering for us endless function on the limited set of examples), and thus any direct or even moderate solutions of this paradox would be focused to its elimination. Thus proved that including for the field of finite functions and languages described theirs the skeptical force of 'rule-following' paradox itself completely saves. Moreover, undertaken in this article analysis detects a very quaint phenomenon to the field of language registers 'Ad finitum' - the effect of 'replication' (in the using of a linguistic phrase is always a n-th set of empirically equivalent but logically incompatible and even non-identical languages which it belongs). Study of the phenomenon of replication leads to a number of important remarks on many critics of Saul Kripke's skeptical paradox, in particular the famous Oxford philosopher Gordon Baker and Peter Hacker. Thus the concept of 'community speakers' has been called by Saul Kripke for skeptical solution to paradox of him own cannot be eliminated by the concept of 'share' and 'shareable' languages proposed for this aim by Gordon Baker and Peter Hacker. Despite the criticism the skeptical paradox 'rule-following' by Saul Kripke is still the center of attention and remains influential in modern philosophy of language and the meaning theory. (shrink)

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution is devoted to the basic issues from Wittgenstein to Kripke. Part II will (...) be about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

The paper presents a phenomenological approach to recent debates in the philosophy of language about rule-following and the normativity of meaning, a debate that can be traced to Ludwig Wittgenstein’s Philosophical Investigations but that was given new life with Saul Kripke’s Wittgenstein on Rules and Private Language. Taking a cue from Hannah Ginsborg’s recent work on “primitive normativity,” I use some of Husserl’s own comments about meaning and the status of rules to sketch a solution to Kripke’s rule-following paradox (...) by appealing to a kind of normativity at the level of perception and intersubjective embodiment. This level of normativity arises, like Ginsborg’s, via a primitive kind of judgment that does not presuppose linguistic or conceptual mastery. Unlike for Ginsborg, however, for Husserl this level should still be understood in terms of meaning—just not in the standard linguistic or conceptual senses prominent in the Anglo-American philosophical tradition in which the rule-following debates have occurred. My interpretation thus also demonstrates how Husserl’s account bypasses certain presuppositions about meaning common in the period of the linguistic turn—presuppositions also questioned, in different ways, by Wittgenstein, by Kripke, and by Ginsborg. (shrink)

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution was devoted to the basic issues from Wittgenstein to Kripke. Part II is (...) about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

The article contains a critical analysis of the skeptical solution to the rule- following problem. The skeptical solution denies the existence of “superlative” R-facts that would make statements of the form “P means R by ‘+’ ” true. The role of the sources for the meaning of ‘+’ here is played by the patterns of solidarity behavior of members of some community to which P belongs. The correct use of ‘+’ would be one that is approved by the competent majority (...) of this community, and there can be no other sense in which it would be correct or wrong. Boyd’s hypothesis denies the communal character of the ‘+’ meaning. While there are no “superlative” R-facts, there should be C-facts not about the R as the standard that P or its community follows in their practice of using ‘+’, but about whether they do it correctly. The proof of the Boyd hypothesis is based on the example of an imaginary Ω-community, whose agents use a finite set of simple symbols for the needs of their arithmetic: ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’. Each symbol denotes a subset of identical, from the Ω-community point of view, numerical values. The symbol ‘A’ is used, for ex- ample, for a subset of the natural numbers 1, 10, 19, 28, 37, 46, etc.; ‘B’ for 2, 11, 20, 29, 38, 47, etc.; ‘C’ for 3, 12, 21, 30, 39, 48, etc. The Ω-community’s arithmetic uses the only local function ⊕ whose range of values forms a finite set of mathematical propositions {α} that are true. The Ω-community’s arithmetic, like our own, is open to many skeptical challenges. Is there a fact that determines the meaning of ‘⊕’? What do agents do when they calculate with ‘⊕’ (say, solve examples ‘A⊕B = ?’, ‘C⊕E=?’, etc.)? Do they Add, Badd or Dadd? To answer them would require a “superlative” R-fact. For the calculation practice with ‘⊕’, it could be a certain R-fact that determines the only possible order for the sequence of numerals ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’ such that {α} is true. An analysis of the calculation practice using the local arithmetic function ⊕ shows that for it there are no such R-facts that would determine the only correct standard R – even if the agents in the Ω-community were trained in such calculations on a full set of cases for the application of that function. However, for such practice there are C-facts (independent in their existence from R-facts) that make it possible to distinguish between what seems to be right and what is right. The solitary agent P and the Ω-community are in the same position regarding the knowledge of C-facts. The Ω-community’s point of view has no advantage in matters of C-facts knowledge over the solitary agent P’s point of view. The Ω-community arithmetic shows that if a solitary agent P had the suitable knowledge of C-facts about the practice of calculations with ‘⊕’, it would allow him/her to disagree with the not correct answers of other members of the community even when they would constitute an absolute majority. (shrink)

Предлагается виттгенштайновское решение скептического парадокса Крипке, который возникает в результате пренебрежения прагматикой и нормативным измерением производимых операций. Парадокс Крипке указывает на то, что натурализация смысла и проблемы следования правилу в рамках классического (ненормативного) натурализма невозможна. Анализируется и критикуется недавно предложенная Гинзборг интерпретация парадокса. Хотя её натуралистический «срединный путь» между диспозиционализмом и ментализмом и близок к нормативному виттгенштайновскому натурализму, вводимое ею понятие примитивной нормативности неудовлетворительно. Правильнее говорить не о натурализме с минимальным добавлением нормативности, как это делает Гинзборг, а о нормативном натурализме.

This thesis is a critical and comparative study of four commentators on the later Wittgenstein’s rule following considerations. As such its primary aim is exegetical, and ultimately the thesis seeks to arrive at an enriched understanding of Wittgenstein’s work through the distillation of the four commentators into what, it is hoped, can be said to approach a definitive interpretation, freed of their individual frailties. -/- The thesis commences by explicating the position of Kripke’s Wittgenstein. He draws our attention to the (...) ‘sceptical problem’ of how we are to resolve the apparently paradoxical situation that whilst we seem to use language meaningfully, there is no fact about us that constitutes our meaning one thing as opposed to something else, and consequently the possibility of our actually meaning anything seems to evaporate. Kripke interprets Wittgenstein as accepting the validity of the sceptical problem, but seeking to establish that the force of the problem is radically diminished because the justification which it has shown to be unobtainable is actually unnecessary for rule following to take place. -/- McDowell tries to show that Kripke is mistaken when he views Wittgenstein as endorsing scepticism in this way, because he sees Kripke as failing to appreciate a section of Philosophical Investigations which suggests that one ought to reject the sceptical paradox by correcting the misunderstanding which gives rise to it. McDowell reads Wittgenstein’s claim as being that we mistakenly think we are caught in a dilemma which requires us either to endorse the sceptical paradox or to subscribe to a mythological picture of rule following; whereas, so the thought goes, we must reject the entire dilemma. -/- Although McDowell’s criticism of Kripke is essentially correct, he is motivated to that criticism by an incorrect reading of Wittgenstein. Central to this misinterpretation is his failure to note Wittgenstein’s belief that universal scepticism is nonsensical. Winch does much to flesh out the nature of Wittgenstein’s claim here, although he makes the mistake of attributing to Kripke that position which the latter finds in Philosophical Investigations. Despite inheriting this error from Winch, Diamond nonetheless improves on his attempt to characterize the shortcomings of Kripke’s reading as an interpretation of Wittgenstein, enabling the thesis to reach a conclusion about Wittgenstein’s understanding of rule following. (shrink)

In this paper, I present a game-theoretic solution to the rule-following paradox in terms of what I will call basic constitutive practices. The structure of such a practice P constitutes what it is to take part in P by defining the correctness conditions of our most basic concepts as those actions that lie on the correlated equilibrium of P itself. Accordingly, an agent S meant addition by his use of the term ‘+’ because S is taking part in a (...) basic constitutive practice of adding where quus-like answers are ruled out by not lying on the equilibrium. The resulting picture of language will preserve the objectivity and correctness conditions of meaning, all the while providing room for the community as a whole to make a mistake. I also argue that by accepting the account presented, we have a strong reason to reject the idea that language is rule-governed. (shrink)

This paper argues that most of the alleged straight solutions to the sceptical paradox which Kripke ascribed to Wittgenstein can be regarded as the first horn of a dilemma whose second horn is the paradox itself. The dilemma is proved to be a by‐product of a foundationalist assumption on the notion of justification, as applied to linguistic behaviour. It is maintained that the assumption is unnecessary and that the dilemma is therefore spurious. To this end, an alternative conception (...) of the justification of linguistic behaviour is outlined, a conception that vindicates some of the insights behind Kripke's Wittgenstein's sceptical solution of the paradox. This alternative conception is defended against two objections (both familiar from McDowell's works): (1) that it would imply that for the linguistic community there is no authority, no standard to meet and, therefore, no possibility of error and (2) that it would lead to a kind of idealism. (shrink)

The paper defends the argument that the Resemblance Paradox (RP), or the problem of the ‘under-determination of meaning’, and the Rule-Following Paradox (RFP) are two sides of the same paradox threatening meaning from opposite extremes. After presenting the case, the paradox is reconsidered anew and the supposition that the threat is a pervasive one is challenged.

The paper puts forward a new skeptical solution to Kripke’s Wittgenstein’s rule-following paradox, a solution which revolves around the idea that human communication does not require meaning facts - at least as defined by Kripke. After a brief discussion of the paradox, I explain why I think that Kripkenstein’s solution needs revision and argue that the main goal of a skeptical solution to the rule-following paradox should be that of showing that communication does not require meaning. After (...) that, I offer two arguments for the thesis that communication does not require meaning. The first argument instantiates a rather direct strategy and focuses on the description of a concrete case of communication without meaning. The second one is more indirect in that I start by describing a world in which, although there are meaning facts, communication does not depend on them. The paper’s last section deals with the issue of meaning talk. (shrink)

Reading Kripke's "Wittgenstein on Rules and Private Language", at first one can easily get confused about his claim that the problem discovered was a sort of ontological skepticism. Contrary to the opinion of a great number of contemporary philosophers who hold that rule-following brings up merely epistemological problems I will argue that the scepticism presented by Kripke really is ontological because it is concerned with the exclusion of certain facts. The first section in this paper is dedicated to a presentation (...) of Kripke's paradox with a clarification of the position of "plus/quus-talk" in the argument. Section two is engaged in one of his classical direct solutions: the dispositional theory which will serve as a preparation for the last section. Section three is concerned with Kripke's solution to the skeptical problem, ending with the question of whether he is giving a real solution. In section four, I will try to give an answer to those questions, distinguishing between two different versions of the problem given by the paradox; a wrong one and a correct one. Readers who are really fed up with the sceptical problem and its sceptical solution can skip section one, two and three, concentrating instead on my own argument for the real nature of the problem. In section five, I will pick up on some ideas from Norwich, who tries to give a "straight solution" to the paradox reanimating some weaker version of a dispositional theory of meaning. I will argue that Horwich's solution is misleading because he aims at the wrong version of the paradox. (shrink)

In the present article, I attempt to relate Saul Kripke's “sceptical paradox” to some issues about the self; specifically, the relation between the self and its mental states and episodes. I start with a brief reconstruction of the paradox, and venture to argue that it relies crucially on a Cartesian model of the self: the sceptic regards the Wittgensteinian “infinite regress of interpretation” as the foundation of his challenge, and this is where he commits the crucial mistake. After (...) the diagnosis, I attempt to sketch my own model of the self and its mental states and episodes. This tentative picture binds meaning and the self together, stressing the subjective aspect of meaning without committing the same fallacy. The solution ventured here is relatively independent of the secondary literatures on the sceptical paradox of following rules, for it aims to provide a new angle to understand and meet the challenge presented by the sceptic. (shrink)

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic (...) and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning. (shrink)

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will lose. I present (...) two objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (shrink)

According to the received view the later Wittgenstein subscribed to the thesis that speaking a language requires being guided by rules (thesis RG). In this paper we question the received view. On its most intuitive reading, we argue, (RG) is very much at odds with central tenets of the later Wittgenstein. Giving up on this reading, however, threatens to deprive the notion of rule-following of any real substance. Consequently, the rule-following considerations cannot charitably be read as a deep and subtle (...) defense of (RG) against the threat of paradox, as proponents of the received view are wont to do. Instead, we argue, the rule-following considerations provide Wittgenstein's deep and subtle reasons for rejecting the very idea that speaking a language involves rule-guidance. Although Wittgenstein subscribed to (RG) during his middle period writings, his later remarks on rules, far from being a clarification and elaboration of his earlier views, are directed against the claim of the middle period that speaking a language is an essentially rule-guided activity. (shrink)

In this note I present a solution to Kripkenstein’s paradox, based on a very simple argument: (1) natural language and rule-following are empirical phenomena; (2) no case has been described, in real life, of a person who behaves as Wittgenstein’s or Kripke’s fictional character; (3) therefore, the discussion of such a case is completely devoid of interest. I lay out the example of a ‘Kripkensteinian apple’, which has a normal weight on even days and is weightless on odd days, (...) in order to highlight the contrast between a genuinely empirical perspective, such as that of physics, and the logical-analytical perspective, under which Kripkenstein’s paradox has attracted so much attention. (shrink)

I argue in the paper that the conception of family resemblance discussed by Ludwig Wittgenstein in Philosophical Investigations is a result of the application of Wittgenstein’s general argument against rule‑following to the pragmatics of all concepts. My argument runs as follows: First, (1) I criticize interpretations of family resemblance as a ‘local’ theory, applicable only to some concepts. Next, (2) I present and criticise a classic argument against the conception of family resemblance. In the following section, (3) I analyse (...) attempts to explicate family resemblance in terms of their possessing a common basic feature. I end my paper (4) by summarizing conclusions drawn from this critical review of literature and I briefly point to a possible solution of the difficulties generated by the concept of family resemblance. (shrink)

It is widely thought that, in §201 of the Philosophical Investigations, Wittgenstein reveals himself to oppose a definite view or theory of rule-following. I argue that, due to the self-undermining character of that section, no such interpretation should be accepted. Then I sketch a reading of Wittgenstein’s method that accounts for the paradoxical nature of §201, and I show how this methodology is realized in his remarks on following a rule.

This paper deals with Veronica Rodriguez-Blanco’s answer to the paradox of the normativity of law: How can autonomous self-legislating persons act, without compromising their autonomy and their will, following legal rules? Regarding Rodriguez-Blanco’s answer, I offer two main critiques. The first one is based on Rodriguez-Blanco’s comments to David Enoch’s paper in which I argue against the idea that a descriptive theoretical account of law can, and should, give an answer to general problems of normativity due to the fact (...) that a theoretical approach that engages in questions about the normativity of law cannot be purely descriptive, therefore against Rodriguez-Blanco I conclude that Enoch’s answer is the only response a descriptive account is able to offer. The second criticism focuses on Rodriguez-Blanco’s response to the paradox and argues that her solution is not, in fact, a descriptive one, but one that relies on strong normative premises, which as it turns out defend a perfectionist perspective towards the law.Resumen:Este trabajo analiza la respuesta que Veronica Rodriguez-Blanco propone para resolver la paradoja de la normatividad del derecho: ¿Cómo es posible que una persona autónoma actúe siguiendo los mandatos de normas jurídicas sin comprometer su autonomía ni su voluntad? El autor ofrece dos críticas a la respuesta de Rodriguez-Blanco. La primera de ellas está basada en los comentarios que Rodriguez-Blanco ha hecho sobre la propuesta de David Enoch. En este punto, el autor argumenta en contra de la idea según la cual una perspectiva descriptiva del derecho puede, y debe, tratar de responder a los problemas generales de la normatividad del derecho. De acuerdo con el autor, una perspectiva que pretenda dar respuesta a los problemas de la normatividad del derecho no puede ser una perspectiva puramente descriptiva. En este sentido, el autor sostiene que la respuesta que ofrece Enoch es la única respuesta que una perspectiva descriptiva del derecho puede dar. La segunda crítica está dirigida a la respuesta que Rodriguez-Blanco da sobre la paradoja de la normatividad. En este segundo punto el autor argumenta que la perspectiva de Rodriguez-Blanco no es una perspectiva descriptiva como ella presume, sino que adopta una perspectiva normativa la cual, además, está comprometida con una idea perfeccionista del derecho. (shrink)

A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out (...) of the paradox. (shrink)

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.

This essay is an inquiry into John McDowell’s thinking on ‘subjectivity.’ The project consists in two parts. On the one hand, I will discuss how McDowell understands and responds to the various issues he is tackling; on the other, I will approach relevant issues concerning subjectivity by considering different aspects of it: a subject as a perceiver, knower, thinker, speaker, agent, person and (self-) conscious being in the world. The inquiry begins by identifying and resolving a tension generated by the (...) very idea of ‘rational animal’: human beings are at the same time natural and rational. Later the inquiry proceeds by considering how McDowell’s notion of ‘second nature’ enables us to be human subjects with many faces. By going through the diagnoses and responses of McDowell, two central problems in modern and contemporary philosophy – the narrow conception of nature and the Cartesian inner space model – are identified and repelled. In Episode N I first urge that we should leave room for a certain notion of ‘world.’ I further argue that mentality has many aspects, and to understand those aspects is to understand the many faces of human subject. In Episode Ⅰ the Aristotelian notion of ‘second nature’ is discussed in order to resolve the tension in the very idea of ‘rational animal.’ Later I reply to some worries about this maneuver, including the objection from Crispin Wright. Hans-Georg Gadamer’s distinction between world and environment is introduced and related to McDowell’s thinking. Episode Ⅱ discusses perception and knowledge; McDowell’s main target – the Cartesian inner space – is introduced and criticized. Barry Stroud’s and Simon Blackburn’s positions are evaluated. Later I connect the main theme of Mind and World to the present context; in particular, I discuss McDowell’s invocation of Donald Davidson and Immanuel Kant. And then I discuss a common accusation of idealism, and Robert Brandom’s accusation of ‘residual individualism.’ Episode Ⅲ concentrates on Saul Kripke’s Wittgenstein, arguing that the master thesis behind the rule-following paradox is a version of the inner space model, and that Kripke’s Wittgenstein is not Wittgenstein. Martin Kusch’s objections are answered; Michael Dummett’s demand of reductionism is rebutted. After this, I turn to Davidson’s ‘no language’ claim, and discuss to what extent McDowell agrees with him. In Episode Ⅳ I evaluate objections from Hubert Dreyfus concerning action and agency. I discuss how Dreyfus and Maurice Merleau-Ponty commit ‘the Myth of the Disembodied Intellect’ identified by McDowell. I answer Michael Ayer’s charge of intellectualism in passing. Later I bring in McDowell’s objections to Derek Parfit on personhood and to Davidson on the mind-body relation. In Episode Ⅴ I focus on consciousness and self-consciousness. McDowell applies his argument against Parfit to Kant, but Maximilian de Gaynesford dissents. I reply to his objections on McDowell’s behalf. I further connect this to McDowell’s attacks on the dualism of scheme and content. This leads to my McDowellian rejection to the existence of qualia, and further brings me to the debate between intentionalism and disjunctivism in the context of the argument from illusion. I argue against Tim Crane’s ways of conceiving issues about intentionalism and the argument from illusion. Varieties of disjunctivism are also discussed. In my Epilogue, I express my worry about McDowell’s notion of ‘self-determining subjectivity.’ According to McDowell, human freedom consists in causations in the space of reason, but as Richard Gaskin points out, a satisfying story of it is yet to be provided. I close this essay with some rough ideas about how to fill in the details of the McDowellian picture. (shrink)

Peter Godfrey-Smith writes in the section 3.3 “The Ravens Problem” of his book “Theory and Reality” [chapter “Induction and Confirmation”]: “First, the logical empiricists were concerned to deal with the case where generalizations cover an infinite number of instances. In that case, as we see each raven we are not reducing the number of ways in which the hypothesis might fail”. Infinite sets and finite sets have different properties and follow different rules. For example: let’s call “bag X” a specific (...) bag that contains 90 marbles; the generalization A “All marbles in bag X are red” covers a finite number of instances. By contrast, the generalization AE “All things that are not red are not marbles in bag X” covers an infinite number of instances. The propositions A and AE are logically equivalent, but there is an asymmetry due to the fact that A can only have a finite number of instances (since the set of the marbles contained in bag X is a finite set). Because of the aforementioned asymmetry, even though A and AE are logically equivalent propositions, it is wrong to equate an instance of A with an instance of AE. Another example involving a finite set: let’s call “barrique X” a certain 205-liter (54.1553 US gal) barrique. In the following generalization, the expression "all minerals" should not be understood as "all types of minerals", but should be understood literally as "all minerals". B “All minerals are in barrique X”. BE “All objects that are not in barrique X are not minerals”. Of course, a 205-litre barrique cannot contain an infinite number of minerals; the set of objects contained in barrique X is a finite set: therefore in the generalization B we refer to a set that is assumed to be an infinite set (the set of minerals) and to a set (the finite set of minerals contained in barrique X) that is not assumed to be an infinite set. By contrast, in the generalization BE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not contained in barrique X and the set of all objects that are not minerals). Therefore, although B and BE are logically equivalent propositions, an instance of BE cannot be equivalent to an instance of B. Now, let’s analyze the following generalizations. C “All the elements of the set of ravens are elements of the set of black ravens”. CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens”. It is assumed that the number of ravens is infinite, but it is not assumed that the number of black ravens is infinite: that the number of black ravens is infinite is only a hypothesis (for which confirmation is sought), it cannot be assumed as true that the number of black ravens is infinite. Therefore, in the generalization C we refer to a set that is assumed to be an infinite set (the set of ravens) and to a set (the set of black ravens) that is not assumed to be an infinite set. By contrast, in the generalization CE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not elements of the set of black ravens and the set of all objects that are not elements of the set of ravens). Someone could argue that in the generalizations C “All the elements of the set of ravens are elements of the set of black ravens” and CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” only the set of ravens is assumed to be infinite: but even in this case an asymmetry would remain because C “ All the elements of the set of ravens are elements of the set of black ravens” refers to a set (the set of ravens) that is assumed to be an infinite set and to a set (the set of black ravens) that is not assumed to be infinite; by contrast, CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” in this case would refer to two sets that are not assumed to be infinite sets. Because of the aforementioned asymmetries, an instance of C cannot be equivalent to an instance of CE. -/- -/- . (shrink)

In Philosophical Investigations §§185–201, Wittgenstein addresses an oscillation in our thinking about the nature of rules. He seems to introduce a problem—how do we follow rules?—, and a “paradox” in which it is rooted, in order to find a solution to them; only to then call the whole puzzle a “misunderstanding” after all. My contention is that this apparent friction can best be understood and resolved when we view it in light of Wittgenstein’s engagement with limits and limitations, and (...) how easy it is to confuse one with the other when thinking about human thought and language. This central bit of the frequently discussed “rule-following considerations,” then, is concerned not simply with matters of semantics, convention, or community, but rather with the question of a proper philosophical method for thinking about our life with language in general. When traced out, these few remarks elucidate a bifurcation in interpreting one of the central methodological themes in Wittgenstein. (shrink)

The paradox of rule-following that Saul Kripke finds in Wittgenstein’s Philosophical Investigations purports to show that words and thoughts have no content—that there is no intentionality. This paper refutes the paradox with a dilemma. Intentional states are posited in rational explanations, which use propositional attitudes to explain actions and thoughts. Depending on which of the two plausible views of rational explanation is right, either: the paradox is mistaken about the a priori requirements for content; or, a fatal (...) flaw in content ascription alleged by the paradox is not a flaw at all, but a necessary component of the proper method of propositional-attitude ascription. On either lemma, rational explanation defuses the paradox. (shrink)

In chapter 3 of Wittgenstein on Rules and Private Language, Kripke’s Wittgenstein offers a “sceptical solution" to the sceptical paradox about meaning developed in chapter 2 (according to which there are no facts in virtue of which ascriptions of meaning such as “Jones means addition by ‘+’” can be true). Although many commentators have taken the sceptical solution to be broadly analogous to non-factualist theories in other domains, such as non-cognitivism or expressivism in metaethics, the nature of the sceptical (...) solution has not been well-understood. The main aim of this paper is to advance our understanding of the nature of the non-factualism about meaning proposed in the sceptical solution. It attempts to outline some desiderata that should be respected by interpretations of the sceptical solution and considers two objections raised against it in Barry Stroud’s paper “Wittgenstein on Meaning, Understanding and Community". It attempts to correct misconstruals of the sceptical solution that have been promulgated by Davidson and some of his followers and suggests that the sceptical solution developed by Kripke’s Wittgenstein is best viewed as a form of quasi-realism about meaning. It ends by outlining what it takes to be the most pressing challenges facing the sceptical solution. (shrink)

Kripkenstein’s challenge is usually described as being essentially about the use of a word in new kinds of cases ‒ the old kinds of cases being commonly considered as non-problematic. I show that this way of conceiving the challenge is neither true to Kripke’s intentions nor philosophically defensible: the Kripkean skeptic can question my answering “125” to the question “What is 68 plus 57?” even if that problem is one I have already encountered and answered. I then argue that once (...) the real nature of Kripkenstein’s challenge is properly appreciated, one extremely popular strategy to try to meet it, what usually goes by the name of “semantic dispositionalism”, loses much of its appeal. Along the way, I also explain that Kripkenstein’s challenge is actually two distinct challenges ‒ one concerning the mental state of meaning, or intending, something by a sign and the other concerning the meaning (referentially conceived) of linguistic expressions. (shrink)

From my ongoing "Metalogical Plato" project. The aim of the diagram is to make reasonably intuitive how the Socratic elenchos (the logic of refutation applied to candidate formulations of virtues or ruling knowledges) looks and works as a whole structure. This is my starting point in the project, in part because of its great familiarity and arguable claim to being the inauguration of western philosophy; getting this point less wrong would have broad and deep consequences, including for philosophy’s self-understanding. -/- (...) (i.) is the first pass at elenchos in which the Socratic interlocutor does not reflect on knowledge being the crux of the problem. (ii.) is the second, rarer, reflective pass in which they are, making the investigation explicitly about knowledge. Its centrality in the Charmides makes that neglected dialogue of superlative importance. This structure is also the gateway through which the discussion/dialectic crosses into the Agathology (discussion of the form of the good) at Republic 505. -/- The problem of elenchos, then, grasped as a whole structure, is that it seems that knowledge can neither satisfactorily be included in nor excluded from its own scope. The development of the ti esti (“what is ---?”) question leads to the introduction of knowledge into its own scope (i. implicitly, as goodness contrasted with blind rule-following ii. explicitly qua knowledge) while the development of the dual peri tinos (“----about what?) question leads to K’s elimination from its own scope. The introductions are motivated to avoid contradiction, but produce regress; the eliminations are motivated to avoid regress, but produce contradiction. In scholarship, and in the history of philosophy, the ti esti question is universally recognized, to the point of being identified with philosophy’s origin and essence; the peri tinos question is neglected textually and never recognized as the equal dual to the ti esti. This, I claim, has blocked the development of a nontrivial logical appreciation of what Plato's Socrates is up to. (One rather disastrous effect of this neglect is taking Aristotle as the beginning of the development of logic, rather than, correctly, for the beginning of logic’s fatal separation from mathematics and dialectic.) -/- Further, because of this monopticism of the ti esti, the function of consistency in the elenchos has not been understood, even with respect to the ti esti. The ti esti is actually in search of completeness, given a norm of consistency; the peri tinos is in search of consistency, given a norm of completeness. Only appreciating the two questions as dual allows space in the structure to clarify these different orientations relative to consistency. (And, dually, to completeness, whose function in the elenchos is generally entirely missed by scholars and relegated to discussions of eros; it's not out of place there, of course, but its significance is secured here.) Recognizing the duality of the ti esti and peri tinos questions is thus the royal road, in the Socratic-Platonic context, to catching sight of what we post-Cantorians can recognize as the metalogical duality of consistency and completeness. (The salutary disruptive effects of this Plato-Cantor proximity have, of course, been traced in complementary ways by Badiou.) -/- Note that the diagram is supposed to provide a relatively accessible orientation, not to stand on its own, and certainly not to be the last word on any subject. An important qualification (telegraphed in the previous paragraph) is that what elenchos shows is not finally circular or paradoxical, though the problem first presents as such (stubbornly, obdurately, as "difficult" Plato's Socrates always says with characteristic understatement). What is depicted here is meant, at a first pass, to be the shape of that first presentation, the form of the problem of elenchos, rather than of its solution. It's not an accident that this problem strongly resembles "Russell's paradox" (not Russell's not a paradox.) Problem is to solution as RP is to the diagonal theorems. (shrink)

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (to replace (...) the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

Normativists about belief hold that belief formation is essentially rule- or norm-guided. On this view, certain norms are constitutive of or essential to belief in such a way that no mental state not guided by those norms counts as a belief, properly construed. In recent influential work, Kathrin Glüer and Åsa Wikforss develop novel arguments against normativism. According to their regress of motivations argument, not all belief formation can be rule- or norm-guided, on pain of a vicious infinite regress. I (...) argue that the regress of motivations argument is unsuccessful: an appeal to the notion of blind rule-following, drawn from a plausible interpretation of Ludwig Wittgenstein’s remarks on rule-following, stops the regress of motivations in its tracks. (shrink)

In her seminal article ‘Modern Moral Philosophy’ (1958) Elizabeth Anscombe argued that we need a new ethics, one that uses virtue terms to generate absolute prohibitions against certain act-types. Leading contemporary virtue ethicists have not taken up Anscombe's challenge in justifying absolute prohibitions and have generally downplayed the role of rule-following in their normative theories. That they have not done so is primarily because contemporary virtue ethicists have focused on what is sufficient for characterizing the deliberation and action of the (...) fully virtuous person, and rule-following is inadequate for this task. In this article, I take up Anscombe's challenge by showing that rule-following is necessary for virtuous agency, and that virtue ethics can justify absolute prohibitions. First, I offer a possibility proof by showing how virtue ethics can generate absolute prohibitions in three ways: by considering actions that directly manifest vice or that cannot be performed virtuously; actions that are prohibited by one's institutional roles and practical identities; and actions that are prohibited by the prescriptions of the wise. I then seek to show why virtue ethicists should incorporate rule-following and absolute prohibitions into their theories. I emphasize the central role that rules have in the development of virtue, then motivate the stronger view that fully virtuous agents follow moral rules by considering the importance of hope, uncertainty about consequences, and taking responsibility for what eventuates. Finally, I provide an account of what Anscombe called a ‘corrupt mind’, explaining how our understanding of virtue is corrupted if we think that virtue may require us to do vicious actions. (shrink)

This paper argues that the problematic of rule following in Wittgenstein's Philosophical Investigations and Heidegger's analysis of anxiety in Being and Time have analogous structures. Working through these analogies helps our interpretation of both of these authors. Contrasting sceptical and anti-sceptical readings of Wittgenstein helps us to resolve an interpretive puzzle about what an authentic response to anxiety looks like for Heidegger. And considering the importance of anxiety to Heidegger's conception of authenticity allows us to locate in Wittgenstein's later philosophy (...) a covert appeal to something resembling Heideggerian authenticity. (shrink)

I address the question of whether naturalism can provide adequate means for the scientific study of rules and rule-following behavior. As the term "naturalism" is used in many different ways in the contemporary debate, I will first spell out which version of naturalism I am targeting. Then I will recall a classical argument against naturalism in a version presented by Husserl. In the main part of the paper I will sketch a conception of rule-following behavior that is influenced by Sellars (...) and Haugeland. I will argue that rule-following is an essential part of human nature and insist in the social dimension of rules. Moreover, I will focus on the often overlooked fact that genuine rule-following behavior requires resilience and presupposes an inclination to calibrate one's own behavior to that of the other members of the community. Rule-following, I will argue, is possible only for social creatures who follow shared rules, which in turn presupposes a shared (first-person plural) perspective. This implies, however, that our scientific understanding of human nature has to remain incomplete as long as it does not take this perspective, which prima facie seems alien to it, into account. (shrink)

This paper employs some outcomes (for the most part due to David Lewis) of the contemporary debate on the metaphysics of dispositions to evaluate those dispositional analyses of meaning that make use of the concept of a disposition in ideal conditions. The first section of the paper explains why one may find appealing the notion of an ideal-condition dispositional analysis of meaning and argues that Saul Kripke’s well-known argument against such analyses is wanting. The second section focuses on Lewis’ work (...) in the metaphysics of dispositions in order to call attention to some intuitions about the nature of dispositions that we all seem to share. In particular, I stress the role of what I call "Actuality Constraint". The third section of the paper maintains that the Actuality Constraint can be used to show that the dispositions with which ideal-condition dispositional analyses identify my meaning addition by "+" do not exist (in so doing, I develop a suggestion put forward by Paul Boghossian). This immediately implies that ideal-condition dispositional analyses of meaning cannot work. The last section discusses a possible objection to my argument. The point of the objection is that the argument depends on an illicit assumption. I show (1) that, in fact, the assumption in question is far from illicit and (2) that even without this assumption it is possible to argue that the dispositions with which ideal-condition dispositional analyses identify my meaning addition by "+" do not exist. (shrink)

Abstract The paper explores responses to an inconsistent quartet of theses regarding rule-following. In addressing this inconsistent quartet, two lines of thought pull in opposite directions. On the one hand, it can seem that rule-following cannot require acts that shape or guide themselves or acts that require infinitely many similar acts. On the other hand, rule-following seems to require that we are responsible for our acts of rule-following in a special way. It is difficult to see how these thoughts can (...) be coherently combined. (shrink)

Abstract The paper explores responses to an inconsistent quartet of theses regarding rule-following. In addressing this inconsistent quartet, two lines of thought pull in opposite directions. On the one hand, it can seem that rule-following cannot require acts that shape or guide themselves or acts that require infinitely many similar acts. On the other hand, rule-following seems to require that we are responsible for our acts of rule-following in a special way. It is difficult to see how these thoughts can (...) be coherently combined. (shrink)

The going-on problem (GOP) is the central concern of Wittgenstein's later philosophy. It informs not only his epistemology and philosophy of mind, but also his views on mathematics, universals, and religion. In section I, I frame this issue as a matter of accounting for intentionality. Here I follow Saul Kripke's lead. My departure therefrom follows: first, a criticism of Wittgenstein's “straight” conventionalism and, secondly, a defense of a solution Kripke rejects. I proceed under the assumption, borne out in the end, (...) that statements of rule-following have truth-conditions and are not, as Kripke seems willing to concede, merely "assertible" in circumstances of a specified sort. Ultimately, my goal is to demonstrate that intending can be understood in terms of an individual's dispositions rather than those of the community to which she belongs. (shrink)

In this essay, I seek to demonstrate the interplay of philosophical voices – particularly, that of a platonist voice and a community-agreement-view voice – that drives Wittgenstein’s rule-following dialectic forward; and I argue that each voice succumbs to a particular form of dialectical oscillation that renders its response to the problem of rule-following philosophically inadequate. Finally, I suggest that, by seeing and taking stock of the dilemma in which these responses to the skeptical problem are caught, we can come to (...) appreciate Wittgenstein’s own view of what might constitute a proper a response to the so-called problem of rule-following. This view can be preliminarily characterized by saying that Wittgenstein’s aim is to dissolve the temptation to philosophically rebut the skeptical challenge posed by the rule-following dialectic, an aim he achieves by revealing the semantic emptiness of the apparent sentences that raise the skeptical problem. (shrink)

Ideas on meaning, rules and mathematical proofs abound in Wittgenstein’s writings. The undeniable fact that they are present together, sometimes intertwined in the same passage of Philosophical Investigations or Remarks on the Foundations of Mathematics, does not show, however, that the connection between these ideas is necessary or inextricable. The possibility remains, and ought to be checked, that they can be plausibly and consistently separated. I am going to examine two views detectable in Wittgenstein’s works: one about proofs, the other (...) about meaning and rules. The first is the denial of the objectivity of proof. The second is a conception of meaning stemming from the rule-following considerations. I shall argue that, though Wittgenstein seems to conjoin the two views, they can be, and should be, separated1. (shrink)

This paper explores how realism is crucial in understanding rule-following. The strategy involves starting from what has been achieved by Wittgenstein and others as regards semantic normativity and then applying it to other areas, including moral deliberation. The result shows that realism in rule-following involves not only the weak claim that rules are independent of the individual rule-follower, as conventions are. It involves also the stronger claim that conventional rules are constrained by non-conventional constraints. These constraints depend neither on the (...) individual nor on the group. They arise from the nature of things. Human rule-followers are constrained first by being material beings, secondly by being living organisms, and thirdly by being rational. (shrink)

In this essay I point out parallels between Kant’s theory of aesthetics and Wittgenstein’s discussion of rule following. Although Wittgenstein did not write an aesthetics and Kant did not discuss Wittgensteinian rule-following problems, and although both Kant and Wittgenstein begin at very different starting points and use different methods, they end up dealing with similar issues, namely issues about rules, particularity, exemplarity, objectivity, practice, and as-if statements.

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.

John Broome’s Rationality Through Reasoning is a trail-blazing study of the nature of rationality, the nature of reasoning and the connection between the two. But it may be somewhat misleading in two respects. First, his theory of reasoning is consistent with the meta-propositional view that he rejects; it develops a broadly similar theory but in much greater detail. And while his discussion of rule-following helps to explain the role of rules in reasoning, it does not constitute a response to the (...) classic problem associated with Wittgenstein and Kripke. (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)

Non-cognitivists claim that thick concepts can be disentangled into distinct descriptive and evaluative components and that since thick concepts have descriptive shape they can be mastered independently of evaluation. In Non-Cognitivism and Rule-Following, John McDowell uses Wittgenstein’s rule-following considerations to show that such a non-cognitivist view is untenable. In this paper I do several things. I describe the non-cognitivist position in its various forms and explain its driving motivations. I then explain McDowell’s argument against non-cognitivism and the Wittgensteinian considerations upon (...) which it relies, because this has been sufficiently misunderstood by critics and rarely articulated by commentators. After clarifying McDowell’s argument against non-cognitivism, I extend the analysis to show that commentators of McDowell have failed to appreciate his argument and that critical responses have been weak. I argue against three challenges posed to McDowell, and show that the case of thick concepts should lead us to reject non-cognitivism. (shrink)

The article contains a critical analysis of Wittgenstein’s theory of logical symbolism. According to an influential interpretation, Wittgenstein presented in the Tractatus a new method of solving paradoxes. This method seems a simple and effective alternative to Russell’s type theory. Wittgenstein’s theory of logical symbolism is based on the requirement of clear notation and the context principle: the type of a symbol only “shows” itself in the way we use the signs of our language. The function sign φ(φx) does not (...) express any paradox, because the syntactic rules for its use, written in clear notation, should “show” us that φ(φx) = ψ(φx). Many researchers (Davant, Ishiguro, Mounce, Ruffino, Friedlander, Jolley, Livingston, Ladov, et al.) follow this interpretation. However, the difficulty of such a view on Wittgenstein’s theory of logical symbolism is that there hides the fallacy of petitio principii. Indeed, in examples of a functional sign of the form φ(φx), we are interested not only in the question of whether the functions φ are different symbols, but also in how this functional sign φ(φx) itself excludes the symbolization of the same object by different ways. This interpretation is contrasted with the idea that Wittgenstein’s theory of logical symbolism is in fact a modified analogue of Russell’s simple theory of types. The reciprocality principle becomes the core of Wittgenstein’s theory: the combinatorial potential of the “prototype” of a functional sign is identical to the combinatorial potential of the “prototype” of an argument. According to Wittgenstein, only describing the combinatorial potential of linguistic expressions (symbols) can vanish the illusion of paradoxes. The function cannot be its argument, because the function sign φ(φx) already contains the “prototype” of its argument, “showing” us that φ(φx) = φx. The correctness of this interpretation does not exclude the possibility that the differences between Russell and Wittgenstein are in fact nothing more than façon de parler. (shrink)