I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...) infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. -/- Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects. (shrink)

ABSTRACTIn 1931 Wittgenstein wrote: ‘the limit of language manifests itself in the impossibility of describing the fact that corresponds to a sentence without simply repeating the sentence’. Here, Wittgenstein claims, ‘we are involved … with the Kantian solution of the problem of philosophy’. This paper shows how this remark fits with Wittgenstein's early account of the substance of the world, his account of logic, and ultimately his view of philosophy. By contrast to the currently influential resolute reading of the Tractatus, (...) the paper argues that the early Wittgenstein did not aim at destroying the idea of a limit of language, but that the notion lies at the very heart of Wittgenstein's early view. In doing so, the paper employs and defends the Kantian interpretation of Wittgenstein's early philosophy. (shrink)

I demonstrate that analogies, both explicit and implicit, between Wittgenstein’s discussion of rituals, aesthetics, and psychoanalysis (and, indeed, his own philosophical methodology) suggest that he entertained the idea that Freud’s psychoanalytic project, when understood correctly—that is, as a descriptive project rather than an explanatory-hypothetical one—provides a “surveyable representation” (übersichtliche Darstellung) of certain psychological facts (as opposed to psychological concepts). The consequences of this account are that it offers an explanation of Wittgenstein’s admiration for and self-perceived affinity to Freud, as well (...) as of his apparent “know-nothing approach” to empirical psychology. (shrink)

This paper forges links between early analytic philosophy and the posits of semiotics. I show that there are some striking and potentially quite important, but perhaps unrecognized, connections between three key concepts in Wittgenstein’s middle and later philosophy, namely, complex, rule-following, and language games. This reveals the existence of a conceptual continuity between Wittgenstein’s “early” and “later” philosophy that can be applied to the analysis of the iterability of representation in computer-generated images. Methodologically, this paper clarifies to at least some (...) degree, the nature, progress and promise of an approach to doing philosophy and semiotics from a modally modest perspective that sees in the intellectual products of humanities, and not in unreflective empiricism, the future of scientific development. This hybrid, non-reductionist approach shows, among other things, that semiotic processes are encoded by specific types of complexes in computer-generated images that display iterability in time and space. (shrink)

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)

O presente artigo busca debater a posição de Charles Sanders Peirce e dos primeiros estudantes peirceanos de Lógica (Christine Ladd e O. H. Mitchell nos Studies in Logic, 1883) dentro do debate inspirador da visão da linguagem dentro da Filosofia Analítica, conhecido como “Lingua Universalis contra Calculus Ratiocinator”, cujos primórdios podem ser traçados desde a filosofia de Gottfried Leibniz. Para isso, comparamos esse campo do pensamento peirceano com o debate crucial entre a conceitografia de Gottlob Frege (Begriffsschrift, 1879) e a (...) lógica algébrica de George Boole (An investigation of the Laws of Thought on which are founded the mathematical theories of Logic and Probabilities, 1854). O nosso objetivo principal é observar que esse momento da filosofia peirceana pode ser comparado com o pensamento wittgensteiniano, especialmente em sua nova vertente, chamada New Wittgenstein, que tenta superar a tradicional divisão entre Tractatus Logico-Philosophicus e Investigações Filosóficas. Pela comparação entre pensadores influenciados por C. S. Peirce e a filosofia de Ludwig Wittgenstein, pretendemos abrir caminhos na compreensão do conceito de jogo de linguagem, especialmente em sua gramática e em seus operadores simbólicos, através da observação das funções de verdade [truth functions] e as tabelas de verdade [truth tables] enquanto lógica algébrica. (shrink)

Analysis of quantifiers in Wittgenstein's Tractatus. A critical survey In the Tractatus Logico-Philosophicus, Wittgenstein distinguishes between what can and cannot be said in any language by the general form of propositions. I explain Wittgenstein's method and discuss Robert J. Fogelin's criticism of what he takes to be the incompleteness of Wittgenstein's general form of propositions in his exposition of the 'Naive Constructivism of the Tractatus.' I argue that Fogelin's objection is mistaken, and that, contrary to Fogelin's claim, Wittgenstein's method when (...) properly applied produces all of the well-formed formulas with mixed multiple quantification that Fogelin maintains it cannot provide. I conclude by offering a critical comparison of similar solutions proposed, among others, by P.T. Geach, Scott Soames, and Matthias Varga von Kibéd. (shrink)

Many interpreters of the Tractatus accept that the book endorses an argument for simples based on the reflection that, since complexes exist only contingently, if names referred to complexes the propositions in which they figure would lack sense if their referents went out of existence. More specifically, most interpreters read 2.0211-2.0212 as putting forward this argument. My main goal in this paper is to attack this reading and to put forward an alternative. I argue that there is no good reason (...) for thinking that the Tractatus advances this argument. I argue that 2.0211-2, in particular, should not be read in this way, and put forward an alternative reading of the passage. (shrink)

The over-arching claim that I intend to defend in this paper is that while widespread ‘local’ error is conceivable, we cannot, in the end, make sense of the radical sceptical idea that all our perceptual beliefs might be false – that no one has, as it were, ever been in touch with an ‘external world’ at all. To this end, I will show that an asymmetry exists between ‘local’ and ‘global’ sceptical scenarios, such that the possibility of ‘local’ error does (...) not imply that ‘global’ error must also be possible. Instead, we will see that what gives rise to the radical sceptical problem is an unquestioned acceptance of the ‘New Evil Genius Thesis’ (NET) – the notion that I and my ‘envatted’ counterpart share the same perceptual experiences, even though my benighted twin has never had any contact with an ‘external’ reality. Although most contemporary epistemologists take NET for granted, I will show that it cannot, ultimately, be rendered intelligible, and, consequently, that neither can the ‘global’ sceptical scenario that depends on it. (shrink)

The paper analyzes the ontological meaning of mood in Heidegger’s conception of Attunement, in order to relate this notion of Stimmung specifically to our “attunement” to a form of life, as conceived in Wittgenstein’s philosophy of language. It claims that moods spell out the constitutive impossibility to grasp and found the human experience as such. However, this impossibility is not a lack of human knowledge, but rather corresponds to the necessary opacity, indeterminability and groundlessness of every human experience, which make (...) it possible as such. The paper argues that the ontological mood of anxiety in Heidegger’s thought cannot be understood as a dark feeling, since it points to a constitutive sense of disorientation, which involves the impossibility to found and ensure the very familiarity of our ordinary experience. Moreover, the paper claims that the same impossibility is also involved in our “attunement” to language and to a form of life, as described by Wittgenstein in his Philosophical Investigations. By analyzing the mood of trust sketched out by Wittgenstein in On Certainty, the paper suggests that the ontological mood of trust, as the groundless certainty of our praxis, points to the very impossibility to found and ensure every human experience. From this perspective, moods reveal the groundlessness of human experience and make us acknowledge it. (shrink)