Assertion plays a crucial dual role in Frege's conception of logic, a formal and a transcendental one. A recurrent complaint is that Frege's inclusion of the judgement-stroke in the Begriffsschrift is either in tension with his anti-psychologism or wholly superfluous. Assertion, the objection goes, is at best of merely psychological significance. In this paper, I defend Frege against the objection by giving reasons for recognising the central logical significance of assertion in both its formal and its transcendental role.

In theTractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, we (...) identify three ways in which the first notational convention can be implemented, show that two of these are compatible with the text of theTractatus, and argue on systematic and historical grounds, adducing posthumous work of Ramsey’s, for one of these as Wittgenstein’s envisaged method. With respect to the second Tractarian proposal, we discuss how Wittgenstein distinguished between general and non-general propositions and argue that, claims to the contrary notwithstanding, an expressively adequate N-operator notation is implicit in theTractatuswhen taken in its intellectual environment. We finally introduce a variety of sound and complete tableau calculi for first-order logics formulated in a Wittgensteinian notation. The first of these is based on the contemporary notion of logical truth as truth in all structures. The others take into account the Tractarian notion of logical truth as truth in all structures over one fixed universe of objects. Here the appropriate tableau rules depend on whether this universe is infinite or finite in size, and in the latter case on its exact finite cardinality.As it is obviously easy to express how propositions can be constructed by means of this operation and how propositions are not to be constructed by means of it, this must be capable of exact expression.5.503. (shrink)

Although the terms ‘poles’, ‘bipolar’, and ‘bipolarity’ do not appear in the Tractatus, it is widely held that Wittgenstein maintained his commitment to bipolarity in the Tractatus. As it is usually understood, the principle of bipolarity is that every proposition must be capable of being true and capable of being false, which rules out propositions that are necessarily true or necessarily false. Here I argue that Wittgenstein was committed to bipolarity in the Tractatus, but getting a clear view of this (...) commitment requires a different understanding of bipolarity. Properly understood, bipolarity is the view that every proposition represents two possible states of affairs, one positive and the other negative. Of course, in the case of elementary propositions, the sense of a proposition is only the positive state of affairs. There is thus an asymmetry between what a proposition represents, its true-false poles, and what it says, its sense. In this paper I show how Wittgenstein accounted for this asymmetry in Notes on Logic and I consider two ways he might have accounted for it in the Tractatus. (shrink)

In this essay I focus on the idea of the univocity of being, championed by Duns Scotus and given prominence more recently by Deleuze. Although I am interested in how this idea can be established, my primary concern is with something more basic: how the idea can even be properly thought. In the course of exploring this issue, which I do partly by borrowing some ideas about logical syntax from Wittgenstein's Tractatus, I try to show how there can be dialogue (...) between analytic philosophers and those of other traditions. (shrink)

Name der Zeitschrift: Nordic Wittgenstein Review Jahrgang: 2 Heft: 1 Seiten: 33-56.

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

It is generally considered the case that an authorial preface is an author’s opportunity to give the reader a hand in interpreting the work he or she is about to read. It is strange then that the Preface to Wittgenstein’s Tractatus (1922) has often been overlooked. Max Black’s (1964) influential A Companion toWittgenstein’sTractatus, for example, passes over the Preface in silence. And even in the latest published edition of the so-called Prototractatus (1996), the Preface is the only part that appears (...) in hand-written facsimile but is not reproduced in typescript form. Perhaps an argument for not so-reproducing the Preface of the Pro- totractatus in typescript is also an argument for the importance of the Preface: not one letter of this early hand-written text of the Preface is different from the final published edition (I will return to this later). Only of late has the Preface to the Tractatus been seen as having any kind of focal importance.This recent interest in the Preface has largely been spawned by Cora Diamond’s and James Conant’s “New” view of Wittgenstein. This New view (designated as such subsequent to the publication in 2000 of the volume entitled The New Wittgenstein) uses the Preface as a central interpretive tool that, according to this view, shows that the Tractatus takes “a strong anti-metaphysical stand” which is “most explicit in Wittgenstein’s statements in the book’s Preface and concluding remarks.1”The third and fourth paragraphs of the Preface are seen as especially revealing of Wittgenstein’s anti-metaphysical purpose. (shrink)

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

A framework is developed for understanding what is “taken for granted” both in philosophy and in life generally, which may serve to orient philosophical inquiry and make it more effective. The framework takes in language and its development, as well as mathematics, logic, and the empirical sphere with particular reference to the exigencies of life. It is evaluated through consideration of seven philosophical issues concerned with such topics as solipsism, sense data as the route to knowledge, the possible reduction of (...) geometry to logic, and the existence and status of human rights. Various dichotomies and the notion of continuity are evidently highly strategic. (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)

Wittgenstein’s project in the Tractatus was to replace Frege-Russell propositions with a new conception capturing the essence of representational thought and language. This, he believed, was philosophy’s only real task. I argue that his account of atomic propositions was an incomplete realization of valuable insights, which, had they been slightly revised, could have been extended to all tractarian propositions. Had Wittgenstein followed this path, he would have made discoveries in the study of language and mind that are only beginning to (...) emerge today. However, doing so would have meant stripping the Tractatus of its pretensions of fundamentally remaking philosophy. (shrink)

I aim to present a solution to the apparent paradox of the Tractatus by means of a minimalist reading grounded in the idea that the correct logical symbolism alone “finally solves” in essentials the philosophical problems. I argue that although the sentences of the Tractatus are nonsensical, rules presented in its symbolism are not. The symbolism itself expresses only a priori rules of logic through schematic variables that do not say anything. I argue that this reading correctly expresses the ladder (...) structure of the book, and that it can account for Wittgenstein's critique of the Tractatus in Some Remarks on Logical Form. (shrink)

This paper is more than a plea for Rhees’ reading of the work of Wittgenstein (particularly of On Certainty). My interest in Rhees’ interpretation lies on its resemblance with my own reading, on the one hand, and on its being (surprisingly) unmentioned by other interpreters, on the other. The two core aims of this paper focus on Rhees’ main ideas. First, I argue that although certain facts that are accepted beyond doubt belong to the method, which in turn is included (...) in grammar, this does not mean that these facts are expressions of rules of grammar. Second, I argue that grammar is not conditioned by a certain class of facts (i.e. general facts of nature), but a language-game is possible because we do not call in question certain facts (i.e. grammar is not conditioned by something like ontology). The point is that those facts that are not called in question are beyond truth and falsity, but this does not mean that these facts must be true. The logical role these facts (and the sentences used to express them) play in a language-game is not that of being true or false. Moreover, grammar itself constitutes what is meant by ‘object’, ‘fact’, or ‘general fact of nature’. (shrink)

Drawing on recent work on the nature of the numbering system of the _Tractatus_ and Wittgenstein’s use of that system in his composition of the _Prototractatus_, the paper sets out the rationale for the online tool called__ __ The University of Iowa Tractatus Map. The map consists of a website with a front page that links to two separate subway-style maps of the hypertextual numbering system Wittgenstein used in his _Tractatus_. One map displays the structure of the published _Tractatus_; the (...) other lays out the structure of the _Prototractatus_. The site makes available the full text of the German and the two canonical English translations.__ __While we envisage the map as a tool that we would like a wide variety of readers to find helpful, we argue that our website amounts to a radically new edition of Wittgenstein’s early masterpiece, with far-reaching implications for the interpretation of that text. In particular, we claim that our visually compelling presentation of the book’s overall structure delivers on Wittgenstein’s cryptic claim in a letter to his publisher that it is the numbers that “make the book surveyable and clear”. (shrink)

One of the unconventional features of Wittgenstein’s _Tractatus Logico-Philosophicus_ is its use of an elaborated and detailed numbering system. Recently, Bazzocchi, Hacker und Kuusela have argued that the numbering system means that the _Tractatus_ must be read and interpreted not as a sequentially ordered book, but as a text with a two-dimensional, tree-like structure. Apart from being able to explain how the _Tractatus_ was composed, the tree reading allegedly solves exegetical issues both on the local and the global level. This (...) paper defends the sequential reading against the tree reading. After presenting the challenges generated by the numbering system and the two accounts as attempts to solve them, it is argued that Wittgenstein’s own explanation of the numbering system, anaphoric references within the _Tractatus_ and the exegetical issues mentioned above do not favour the tree reading, but a version of the sequential reading. This reading maintains that the remarks of the _Tractatus_ form a sequential chain: The role of the numbers is to indicate how remarks on different levels are interconnected to form a concise, surveyable and unified whole. (shrink)

No Teeteto, em uma tentativa de denir o conhecimento, Platão trata da unidade e da complexidade segundo um modelo de análise dos complexos em elementos simples não analisáveis. Wittgenstein, no parágrafo 46 das Investigações Filosócas, cita esse argumento do Teeteto, introduzindo uma crítica à sua própria noção de objeto, no Tractatus. Nosso tema será um exame das noções de elemento e composto, apresentadas no Teeteto e retomadas no Sosta, tendo como horizonte a aproximação, feita por Wittgenstein, entre o objeto do (...) Tractatus e o elemento do Teeteto. (shrink)

Review of H. Biesenbach: Anspielungen und Zitate im Werk Ludwig Wittgensteins (2011).

Resumo: Este trabalho busca fazer algumas especulações a respeito de uma das idéias mais controversas presentes na primeira obra de Wittgenstein, a saber, o místico. Tentaremos elucidar este conceito, comparando-o com o misticismo religioso caracterizado por William James em As Variedades da experiência religiosa. Tal comparaçáo se faz necessário, a nosso ver, para que se possa esclarecer algumas peculiaridades do místico tractatiano, desenvolvendo assim, uma percepçáo mais acurada da importância deste conceito dentro do Tractatus. A nosso ver, ele náo é (...) um tema gratuito em tal obra, ao contrário, é decorrência lógica do encontro do sujeito volitivo com os limites da linguagem, apresentados através da análise lógica da proposiçáo. Tentaremos, assim, neste trabalho, elucidar como o místico do Tractatus se assemelha e difere do misticismo religioso. Palavras-chave: James; Místico; Tractatus ; Wittgenstein. (shrink)

In rejecting, In 1929-30, The complete independence of the elementary propositions--According to which any combination of truth-Values for any set of elementary propositions is logically possible--Wittgenstein did not reject an essential element of the "tractatus" system but rather one that fails to cohere with the central picture-Theory of propositions, According to which a method of truth-Valued representation must be capable of presenting 'competing alternative' representations, The false one of these alternatives being false because they fail to 'agree' or 'coincide' with (...) reality, involves an unmotivated rejection of the idea that logical form should exhibit incompatibilities at the atomic level as well as the molecular level, And can be eliminated from the "tractatus" system without eliminating the atomicity of its metaphysics. (shrink)

The power of Wittgenstein's N operator described in the Tractatus is that every proposition which can be expressed in the Russellian variant of the predicate calculus familiar to him has an equivalent proposition in an extended variant of his N operator notation. This remains true if the bound variables are understood in the usual inclusive sense or in Wittgenstein's restrictive exclusive sense. The problematic limit of Wittgenstein's N operator comes from his claim that symbols alone reveal the logical status of (...) propositions. This would require knowledge of the size of the Tractarian domain of unchangeable, simple objects, and this, Wittgenstein maintained, cannot be known. (shrink)

The paper presents a formal explication of the early Wittgenstein's views on ontology, the syntax and semantics of an ideal logical language, and the propositional attitudes. It will be shown that Wittgenstein gave a language of thought analysis of propositional attitude ascriptions, and that his ontological views imply that such ascriptions are truth-functions of (and supervenient upon) elementary sentences. Finally, an axiomatization of a quantified doxastic modal logic corresponding to Tractarian semantics will be given.

The physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von (...) Kries's approach had more potential than recognized in his time and that putting Waismann's and Wittgenstein's early work in a von Kries perspective is able to shed light on the notion of an elementary proposition. (shrink)