In his Tractatus, Wittgenstein sets out what he calls his N-operator notation which can be used to calculate whether an expression is a tautology. In his Laws of Form, George Spencer Brown offers what he calls a “primary algebra” for such calculation. Both systems are perplexing. But comparing two blurry images can reduce noise, producing a focus. This paper reveals that Spencer Brown independently rediscovered the quantifier-free part of the N-operator calculus. The comparison sheds a flood light on each and (...) from the letters of correspondence we shall find that Russell, as one might have surmised, was a catalyst for both. (shrink)

Si decidiésemos clasificar las teorías éticas en “inmanentistas” (aquellas que cifran lo éticamente aceptable en algún tipo de eventos del mundo, como por ejemplo el crecimiento utilitarista del beneficio general) y “trascendentalistas” (aquellas que ubican en algún espacio más allá de este mundo y esta vida el motivo de por qué comportarnos éticamente –por ejemplo, debido a alguna suerte de recompensa ultraterrena–), entonces el pensamiento moral del llamado “primer” Wittgenstein ocuparía un lugar especial entre ambos extremos de tal dicotomía. En (...) cierta medida, podría decirse que la propuesta ética del Wittgenstein que reflexionaba en torno a los años de composición del Tractatus guarda un delicado equilibrio que evita tanto su exclusivo sometimiento ante instancias trascendentales (fundamentos), como su asimilación total por parte de motivaciones inmanentes (provechos) a la hora de justificar el hecho de actuar de un modo correcto. En el presente artículo nos asomaremos a tal pirueta wittgensteiniana entre ambos miembros del dualismo trascendente-inmanente, y sugeriremos que el peculiar lugar en que deja lo ético, entre lo celestial y lo terrenal, acaso no sea del todo ajeno a tesis de la religión cristiana como la de la encarnación de lo divino en el mundo terreno. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)

"Certainty" occupies an important place in Wittgenstein’s epistemology: it does not belong to the category of knowledge but constitutes its foundation. In his view, knowledge boils down to language games, and language games are based on indubitable certainties. According to Wittgenstein, scepticism is meaningless, and if there is no certainty, then even doubt would be meaningless. Wittgesntein maintains that [relative] doubt and knowledge are epistemic categories, whereas absolute doubt and certainty are non-epistemic categories. Epistemic categories are meaningful and when expressed (...) by means of statements could be either true or false. In contrast, non-epistemic categories are meaningless and when expressed by means of statements the properties of truth and falsehood do not apply to them. The aim of the present paper is two fold: 1- Providing an explanation of the status of certainty in comparison to categories such as doubt and knowledge in Wittgenstein’s thought; 2- Providing a critical assessment of Wittgenstein's approach to certainty through the prism of critical rationalism. The main arguments of the paper are as follows: 1. Although Wittgenstein considers certainty to be meaningless and therefore not on a par with epistemological categories, he regards it as an objective concept that functions as the foundation upon which all human knowledge is based; 2. Wittgenstein's efforts to show the objectivity of certainty have not been entirely successful, partly due to his reliance on a defective notion of ‘objectivity’ and partly as a result of the prominence he assigns to the category of ‘meaning’ at the expense of the category of ‘truth’. (shrink)

In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...) a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

The following inquiry pursues two interlinked aims. The first is to understand Wittgenstein's idea of non-foundational certainty in the context of a reading of On Certainty that emphasizes its Pyrrhonian elements. The second is to read Wittgenstein's remarks on idealism/radical skepticism in On Certainty in parallel with the discussion of rule-following in Philosophical Investigations in order to demonstrate an underlying similarity of philosophical concerns and methods. I argue that for the later Wittgenstein, what is held certain in a given context (...) of inquiry or action is a locally transcendental condition of the inquiry or action in question. In On Certainty, Wittgenstein's analysis of the difference between knowledge and certainty forms the basis of his critique of both Moore's "Proof" and radical skepticism. This critique takes the shape of rejection of a presupposition shared by both parties, and utilizes what I identify as a Pyrrhonian-style argument against opposed dogmatic views. Wittgenstein's method in this text involves describing epistemic language-games. I demonstrate that this is consistent with the rejection of epistemological theorizing, arguing that a Wittgensteinian "picture" is not a theory, but an impressionistic description that accomplishes two things: (i) throwing into relief problems with dogmatic theories and their presuppositions, and (ii) describing the provenance of linguistic and epistemic practices in terms of norms grounded in convention. Convention, in turn, is not arbitrary, but grounded in the biological and social natures of human beings--in what Wittgenstein calls forms of life. Thus there is a kind of naturalism in the work of the later Wittgenstein. It is a naturalism that comes neatly dovetailed with Pyrrhonism--a combination of strategies traceable to Hume's work in the Treatise. I read Hume as someone who develops the Pyrrhonian method to include philosophy done "in a careless manner," and argue that Wittgenstein adopts a similar method in his later works. Finally, I explain the deference to convention in the work of both Hume and Wittgenstein by reference to a passage in Sextus' Outlines, on which I provide a gloss in the final chapter of this work. (shrink)

Russell is often accused of having a naive ‘Fido’–Fido theory of meaning of the sort Wittgenstein attacked at the beginning of the Philosophical Investigations. In this paper I argue that he never held such a theory though I concede that, prior to 1918, he said various things that might lead a very careless reader to suppose that he had. However, in The Analysis of Mind, a book which we know Wittgenstein studied closely, Russell put forward an account of understanding an (...) utterance which clearly anticipates the use theory of meaning usually attributed to Wittgenstein. The paper concludes with some problems for understanding the use theory of meaning as presented by both Russell and, derivatively, Wittgenstein. (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)

Drawing Wittgenstein's and Irigaray's philosophies into conversation might help resolve certain misunderstandings that have so far hampered both the reception of Irigaray's work and the development of feminist praxis in general. A Wittgensteinian reading of Irigaray can furnish an anti-essentialist conception of "woman" that retains the theoretical and political specificity feminism requires while dispelling charges that Irigaray's attempt to delineate a "feminine" language is either groundlessly utopian or entails a biological essentialism.

The aim of this paper is twofold. Firstly, it analyses the similarities that stem from Wittgenstein’s (Philosophical Investigations (1953)) and Brandom’s (Making it Explicit (1994)) commitment to pragmatics in the philosophy of language to account for moral utterances. That is, the study of the meaning of moral utterances is carried out resorting to the study of the acts being performed in producing or exhibiting these utterances. Both authors offer, therefore, a pragmatic solution in order to account for the meaning of (...) our moral vocabulary and discursive practices. Secondly, it argues that both approaches lead to differing understandings of the role of “truth” and “falsity” in moral discourse. On the one hand, Wittgenstein’s remarks on ethics demonstrate a dismissive attitude towards the notions of truth and falsity in moral discourse. On the other hand, Brandom seems to be committed to a weak version of moral cognitivism: he takes assertions (which express beliefs, i.e. doxastic commitments) as the fundamental linguistic activity in the game of giving and asking for reasons and provides an anaphoric theory of truth to account for “truth” and “falsity” in our discourse. Additionally, it analyses how these differences bear on the Frege–Geach problem. (shrink)