Many contemporary philosophers rate error theories poorly. We identify the arguments these philosophers invoke, and expose their deficiencies. We thereby show that the prospects for error theory have been systematically underestimated. By undermining general arguments against all error theories, we leave it open whether any more particular arguments against particular error theories are more successful. The merits of error theories need to be settled on a case-by-case basis: there is no good general argument against error theories.

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 paper reviews the grounds for relativist interpretations of Wittgenstein's later thought, especially in On Certainty . It distinguishes between factual and virtual forms of epistemic relativism and argues that, on closer inspection, Wittgenstein's notes don't support any form of relativism – let it be factual or virtual. In passing, it considers also so-called "naturalist" readings of On Certainty , which may lend support to a relativist interpretation of Wittgenstein's ideas, finds them wanting, and recommends to interpret his positive proposal (...) in On Certainty as a form of "internal rationalism.". (shrink)

In Necessary Beings, Bob Hale addresses two questions: What is the source of necessity? What is the source of our knowledge of it? He offers novel responses to them in terms of the metaphysical notion of nature or, more familiarly, essence. In this paper, I address Hale’s response to the first question. My assessment is negative. I argue that his essentialist explanation of the source of necessity suffers from three significant shortcomings. First, Hale’s leading example of an essentialist explanation merely (...) asserts that the nature of an entity explains some necessity, but leaves unexplained how it does so. Second, his essentialist explanation of particular necessities introduces new necessities that remain unexplained. Third, Hale’s version of essentialism presupposes a controversial metaphysical theory of properties, for which he offers no defense. (shrink)

This paper attempts to locate, within an actualist ontology, truthmakers for modal truths: truths of the form or . In Sect. 1 I motivate the demand for substantial truthmakers for modal truths. In Sect. 21 criticise Armstrong's account of truthmakers for modal truths. In Sect. 31 examine essentialism and defend an account of what makes essentialist attributions true, but I argue that this does not solve the problem of modal truth in general. In Sect. 41 discuss, and dismiss, a theistic (...) account of the source of modal truth proposed by Alexander Pruss. In Sect. 5 I offer a means of (dis)solving the problem. (shrink)

Barry Barnes and David Bloor of the Strong Programme of the sociology of knowledge advance a naturalized epistemology that reduces all accounts of normativity to social causes. I endorse their program of naturalizing one kind of normativity, but I argue that there is another kind they cannot naturalize. Within the context of sociological explanations of rationality, there are norms of rationality instantiated by scientists that Barnes and Bloor study, and Barnes and Bloor's own normative ascriptions of scientists as rational beings. (...) I argue that Barnes and Bloor successfully justify their naturalization of the norms of rationality of the scientists they describe by a methodological caution and arguments from under-determination and finitism. But they inevitably fail to naturalize their own normative ascriptions of those scientists as rational. (shrink)

Wittgenstein's conception of logical and conceptual truth is often thought to rival that of the logical positivists. This paper argues that there are important respects in which these conceptions complement each other. Analyticity, in the positivists' sense, coincides, not with Wittgenstein's notion of a grammatical proposition, but rather with his notion of a tautology. Grammatical propositions can usually be construed as analyticity postulates in Carnap's sense of the term. This account of grammatical and analytic propositions will be illustrated by appeal (...) to logical, conceptual and arithmetic truths. Its consequences for an analysis of corresponding modal notions will be indicated. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...) with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

This paper argues that there are three reasons why we should regard Wittgenstein's Tractatus as a forerunner of formal semantics: Wittgenstein is convinced that we can apply formal notions to natur...

In his Remarks on the Foundations of Mathematics, Wittgenstein claims, puzzlingly, that ‘the proof creates a new concept’ (RFM III-41). This paper aims to contribute to clarifying this idea, and to showing how it marks a major break with the traditional conception of proof. Moreover, since the most natural way to understand his claim is open to criticism, a secondary goal of what follows is to offer an interpretation of it that neutralizes the objection. The discussion proceeds by analysing a (...) well-known geometrical proof. (shrink)

My main aim is to sketch a certain reading (‘genealogical’) of later Wittgenstein’s views on logical necessity. Along the way, I engage with the inferentialism currently debated in the literature on the epistemology of deductive logic.

An attempt is made to show that Wittgenstein's later philosophy of logic is not the kind of conventionalism which is often ascribed to him. On the contrary, Wittgenstein gives expression to a “mixed” theory which is not only interesting but tends to resolve the perplexities usually associated with the question of the a priori character of logical truth. I try to show that Wittgenstein is better understood not as denying that there are such things as “logical rules” nor as denying (...) that the results of applying such rules are “logically necessary,” but as trying to understand what it is to appeal to a logical rule and what it means to say that the results of applying such a rule are “necessary.” He is not so much overthrowing standard accounts of logical necessity as discovering the limits of the concept. (shrink)

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...) program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (shrink)

La tesis de la privacidad linguitica nace con el gesto fundador de la filosofía moderna que apoya toda legitimidad en la subjetividad y la conciencia. Ello da origen a dos problemas filos�ficos fundamentales, concernientes al mundo y al solipsismo. El siglo XX creyó encontrar en el lenguaje una salida a estos problemas. Wittgenstein es allí una pieza clave. Sin embargo las interpretaciones más influyentes de Wittgenstein enfocaron la crítica del lenguaje privado de tal modo que la salida debía permanecer en (...) el terreno epistemológico de las garantías o criterio de corrección (Malcolm, Fogelin, Kenny, Canfield, Tugendhat). Sostenemos que la interpretación propuesta por Kripke se apoya un un agudo diagnóstico de la fuente de estas dificultades, dándose cuenta que la refutación del lenguaje privado requería abandonar toda una concepción, la del realismo, que afectaban por igual al lenguaje privado y al público. Su argumentación, centrada en la semántica, irradia consecuencias más allá de la misma. Su "solución escéptica" al establecer que los juicios de corrección, entendidos como básicos y primitivos, sólo poseen sentido en el marco de una comunidad uniforme en sus juicios, coloca al discurso filosófico en un nuevo terreno. (shrink)

In this paper, I take issue with a core commitment of logical conventionalism: that we impose a logic on ourselves by adopting general linguistic conventions governing our use of logical terms, thereby determining the meanings of the logical constants and which of our inferences are valid. Drawing on Kripke’s ‘adoption problem’, I argue that general logical principles cannot be adopted, either explicitly or implicitly. I go on to argue that the meanings of our logical terms, and the validity of our (...) inferences, cannot depend on our adoption of logico-linguistic conventions. (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)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

'Reason, Causation and Compatibility with the Phenomena' strives to give answers to the philosophical problem of the interplay between realism, explanation and experience. This book is a compilation of essays that recollect significant conceptions of rival terms such as determinism and freedom, reason and appearance, power and knowledge. This title discusses the progress made in epistemology and natural philosophy, especially the steps that led from the ancient theory of atomism to the modern quantum theory, and from mathematization to analytic philosophy. (...) Moreover, it provides possible gateways from modern deadlocks of theory either through approaches to consciousness or through historical critique of intellectual authorities. This work will be of interest to those either researching or studying in colleges and universities, especially in the departments of philosophy, history of science, philosophy of science, philosophy of physics and quantum mechanics, history of ideas and culture. Greek and Latin Literature students and instructors may also find this book to be both a fascinating and valuable point of reference. (shrink)

The state of recent as well as older research on social ontology suggests a paradigmatic approach, according to which it is our consciousness that must provide the framework for conceptualising the social. I, however, argue that Wittgenstein’s treatment of rule-following opens up a new horizon for the ontology of the social. The fact that the rules of our language are social in nature and that we need not be aware of them in order to follow them shifts the problem to (...) what lies behind consciousness. The ontological conceptualisation of the social must focus on our implicit knowledge instead, which is always an enabling condition for our consciousness: for we share some of this implicit knowledge with others, as can be seen from Wittgenstein and the case of language. (shrink)

Dummett's objections to the coherence of the strict finitist philosophy of mathematics are thus, at the present time at least, ill-taken. We have so far no definitive treatment of Sorites paradoxes; so no conclusive ground for dismissing Dummett's response — the response of simply writing off a large class of familiar, confidently handled expressions as semantically incoherent. I believe that cannot be the right response, if only because it threatens to open an unacceptable gulf between the insight into his own (...) understanding available to a philosophically reflective speaker and the conclusions available to one confined to observing the former's linguistic practice; for an observer of our linguistic practice could never justifiably arrive at the conclusion that ‘red’, ‘child’, etc., are governed by inconsistent rules. But the Sorites is not the subject of this paper. The points I hope to have made plausible are: that a generalized intuitionist position cannot be so much as formulated and that even a most local intuitionism, argued for the special case of arithmetic, is hard pressed effectively to stabilize and defend itself; that strict finitism remains the natural outcome of the anti-realism which Dummett has propounded by way of support for the intuitionist philosophy of mathematics; that it is powerfully buttressed by the ideas of the latter Wittgenstein on rule-following; and that there is no extant compelling reason to suppose that its involvement with predicates of surveyability calls its coherence into question. The correct philosophical assessment of strict finitism, and its proper mathematical exegesis, remain absolutely open, almost virgin issues. This is not a situation which philosophers of mathematics should tolerate very much longer. (shrink)

Tractatus, 5.62 famously says: ‘… what the solipsist means is quite correct; only it cannot be said but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language mean the limits of my world.’ The later part of this repeats what was said in summary at 5.6: ‘the limits of my language mean the limits of my world’. And the key to the problem ‘how much truth there is in solipsism’ has (...) been provided by the reflections of TLP, 5.61. (shrink)

Tractatus, 5.62 famously says: ‘… what the solipsist means is quite correct; only it cannot be said but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language mean the limits of my world.’ The later part of this repeats what was said in summary at 5.6: ‘the limits of my language mean the limits of my world’. And the key to the problem ‘how much truth there is in solipsism’ has (...) been provided by the reflections of TLP, 5.61. (shrink)

The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the foundations of mathematics. The intuitionistic themes to analyse in his philosophy of mathematics are: firstly, his attacks on the unrestricted use of the Law of Excluded Middle; secondly, his distrust (...) of non-constructive proofs; and thirdly, his impatience with the idea that mathematics stands in need of a foundation. These elements are Fogelin's starting point for the systematic reconstruction of Wittgenstein's conception of mathematics. (shrink)

This article aims to show that Wittgenstein’s remarks on religious belief and religious statements can be understood in modest philosophical terms, consistent with the thought that they are neither intended as serving to justify or undermine religious beliefs, nor as the expression of any theorizing about the nature of religious belief or the meaning of religious language. Instead, their philosophical significance is held to consist in their functioning to remind us of what we already know about the latter: such things (...) as in what circumstances one utters religious statements, what the consequences of accepting or rejecting religious beliefs are, and so on. His position is that all attempts to say something more than this are either a mark of philosophical arrogance or a manifestation of one’s own personal commitment to adopting a stance of religious belief or non-belief. As such, they do not furnish us with genuine philosophical insights. I argue that such an interpretation possess two principal merits. Firstly, it demonstrates that there is no tension between Wittgenstein’s remarks on the nature of philosophy and his remarks on religious belief and religious statements. Secondly, it shows that it is possible to philosophize about religion in a manner that does not assume that this has to consist either in presenting an apology for or critique of religion or in formulating philosophical theories regarding the nature of religious belief and the meaning of religious language. (shrink)

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

Here I defend dispositionalism about meaning and rule-following from Kripkenstein's infamous anti-dispositionalist arguments. The problems of finitude, error, and normativity are all addressed. The general lesson I draw is that Kripkenstein's arguments trade on an overly simplistic version of dispositionalism.

En este trabajo examino el argumento de McFetridge a favor de la necesidad de la creencia en la necesidad. El argumento pretende establecer un dilema fatal para el “nihilista” modal, aquel que no cree que al menos alguna proposición es necesaria. Mi objetivo principal es mostrar que el dilema que presenta el argumento de McFetridge no es sólido, pues tiene una limitación muy importante con respecto al segundo de sus cuernos, el cual es el más interesante. El segundo cuerno del (...) dilema plantea una especie de argumento trascendental: es necesario creer en la necesidad si es que vamos a ser capaces de razonar confiablemente bajo suposiciones contrafácticas. Sin embargo, este argumento asume que la suposición contrafáctica es una actividad esencial en nuestras vidas, lo cual señala, sostengo, un punto central alrededor del cual el nihilista modal intentaría reafirmar su posición. Así, pretendo mostrar que el segundo cuerno del dilema de McFetridge revela que el quid de la discusión entre creyentes y nihilistas modales debe moverse propiamente de la cuestión del rol de la creencia en la necesidad a la cuestión del rol de la suposición contrafáctica. (shrink)

Despite the otherwise-dominant trends towards physicalism and naturalism in philosophy, it has become increasingly common for metaphysicians to accept the existence either of modal facts and properties, or of Lewisian possible worlds. This paper raises the historical question: why did these heavyweight realist views come into prominence? The answer is that they have arisen in response to the demand to find truthmakers for our modal statements. But this demand presupposes that modal statements are descriptive claims in need of truthmakers. This (...) presupposition was, however, rejected by many earlier analytic philosophers, including the logical positivists, Wittgenstein, Ryle and Sellars, all of whom denied that modal statement were descriptive at all. Yet the non-descriptivist approach has largely fallen out of discussion and out of philosophical consciousness. In this paper I examine why non-descriptivist views first came into and then fell out of favor, and consider what the prospects are for reviving this more deflationary approach to modality. (shrink)

SummarySurely, we think, in some cases it is determinate which rules we follow . But what in the world could determine a rule for us in any case? First 1 consider five common, perfectly natural, but utterly inadequate sorts of answer to this question. Then I consider an account which would avoid the usual inadequacies but would leave rules radically indeterminate, a position which is utterly counter‐intuitive. Thus painted into a corner, I then step out with a prima facie queer, (...) but adequate and ultimately not terribly counter‐intuitive, solution to the puzzle: a sort of picture‐theory of understanding rules . Finally 1 show that the picture‐theory undermines the sorts of anti‐realism which would, if they were valid, undermine the picture‐theory.RésuméNous pensons que, dans certains cas, les règies que nous suivons sont sûrement déterminées. Mais qu'est‐ce au monde qui pourrait déterminer pour nous une règie dans tous les cas? Je considère d'abord cinq réponses communes à cette question, réponses très naturelles, mais absolument inadéquates. Ensuite, j'examine une réponse qui serait plus adéquate, mais laisserait les règies radicalement indéterminées, ce qui est très contraire a l'intuition. Je propose alors une solution qui paraît au premier abord saugrenue, mais qui est adéquate et pas tellement contraire à l'intuition: une sorte de theorie des images pour comprendre les régies . Finalement, je montre que cette théorie des images désarme les types d'antiréalisme qui, s'ils étaient valables, s'opposeraient à cette théorie des images.ZusammenfassungWir denken, dass in einigen Fällen bestimmt ist, wetche Regeln wir befolgen . Was aber in der Welt könnte eine Regel in einem beliebigen Fall bestimmen? Ich betrachte zunächst fünf gewöhnliche durch‐aus natürliche, aber völlig inadäquate Arten von Antworten auf diese Frage. Dann betrachte ich eine Behandlung , die die üblichen Mängel vermeidet, die jedoch Regeln radikal unbestimmt lässt, was unserer Intuition zuwiderläuft. So in die Enge getrieben suche ich einen Ausweg in einer Lösung, die prima facie zwar befremdlich erscheinen mag, die aber adäquat ist und nicht stark gegen die Intuition verstösst: eine Art von Bildtheorie des Verstehens von Regeln . Schliesslich weise ich nach, dass die Bildtheorie die Arten von Antirealismus unterminiert, die die Bildtheorie zerstören würden, wenn sie güitig waren. (shrink)

Michael Della Rocca has recently argued that Kripkean essentialism is subtly self-defeating: to defend it, certain modal intuitions must be reconstrued in terms of similarity, but reconstruing them in this way threatens the principled rejection of similarity comparisons on which Kripke's essentialism depends. Della Rocca holds that Kripke's strategy must assume the necessity of identity, and that the necessity of identity already presupposes essentialism, which renders the defence circular. Against this, I argue that the necessity of identity may be accepted (...) independently; therefore no circularity need arise. I also argue that Della Rocca fails to rebut an objection raised by Stephen Yablo. (shrink)

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

This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for (...) the philosophy of mathematical practice will be presented here, including a brief reconstruction of Lakatos’ considerations on Euler’s conjecture for polyhedra from the lens of late Wittgensteinian philosophy. Overall, this article aims to challenge the received view of the history of the philosophy of mathematical practice and inspire further work in this community drawing from Wittgenstein’s late philosophy. (shrink)

This paper portrays the later Wittgenstein’s conception of contradictions and his therapeutic approach to them. I will focus on and give relevance to the Lectures on the Foundations of Mathematics, plus the Remarks on the Foundations of Mathematics. First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: a rejection of the debate about realism and anti-realism in mathematics; and Wittgenstein’s endorsement of logical pluralism. Then, I will explain Wittgenstein’s therapeutic approach towards contradictions, and why it means that (...) a contradiction is not a problem for logic and mathematics. Rather, contradictions are problematic when we do not know what to infer from them. Once a meaning is established through a new rule of inference, the contradiction becomes a usable expression like many others in our inferential apparatus. Thus, the apparent problem is dissolved. Finally, I will take three examples of dissolved contradictions from Wittgenstein to clarify further his notion. I will conclude considering why his position on contradictions led him to clash with Alan Turing, and whether the latter was convinced by the Wittgensteinian proposal. (shrink)

I examine what I take to be an important consideration for the later Wittgenstein: the understanding of a rule does not exceed or transcend an understanding of explanations or instructions in the rule. I contend that this consideration plays a central role in the later Wittgenstein's views on rule-following. I first show that it serves as a key premiss in a sceptical argument concerning our ability to follow rules. I then argue that this consideration is vital to Wittgenstein's case against (...) what I describe as a realist view of rules. This realist view requires that our understanding of a rule extend beyond what can be understood from any set of instructions or explanation. For Wittgenstein, because this is to transcend publicly available means of conveying understanding, this realist's understanding is a private understanding. He calls this private source of understanding an ‘intuition’ and the main line of argument against intuition in our understanding of a rule draws, appropriately, on what is called his ‘private language argument’. In this paper, I defend a non-verificationist reading of this argument and its use against the realist so-construed. CiteULike Connotea Del.icio.us What's this? (shrink)

In the scholarship on Wittgenstein’s later philosophy of mathematics, the dominant interpretation is a theoretical one that ascribes to Wittgenstein some type of ‘ism’ such as radical verificationism or anti-realism. Essentially, he is supposed to provide a positive account of our mathematical practice based on some basic assertions. However, I claim that he should not be read in terms of any ‘ism’ but instead should be read as examining philosophical pictures in the sense of unclear conceptions. The contrast here is (...) that basic assertions that frame philosophical ‘isms’ are propositional such that they are subject to normal argumentative evaluation, while pictures in Wittgenstein’s sense are non-propositional—they lack a clear truth condition. They, therefore, need clarification rather than argumentation. In this paper, I provide a detailed analysis of Wittgenstein’s treatment of philosophical pictures with special focus on his argument on contradiction. I begin by explaining the problem with this trend of theoretical interpretation, taking Steve Gerrard’s otherwise excellent interpretation as a representative example and pointing out why it is problematic. Next, I will argue that those problems do not arise if we take Wittgenstein’s task as the clarification of philosophical pictures. I do this, first, by explaining Wittgenstein’s method using his argument concerning the Augustinian Picture in Philosophical Investigations and then pointing out that the same method can be identified in the crucial arguments in his philosophy of mathematics. Finally, in order to connect my interpretation with the current scholarship, I will explain the relation of my interpretation with those of New Wittgensteinian scholars. (shrink)