Turing was a philosopher of logic and mathematics, as well as a mathematician. His work throughout his life owed much to the Cambridge milieu in which he was educated and to which he returned throughout his life. A rich and distinctive tradition discussing how the notion of “common sense” relates to the foundations of logic was being developed during Turing’s undergraduate days, most intensively by Wittgenstein, whose exchanges with Russell, Ramsey, Sraffa, Hardy, Littlewood and others formed part of the backdrop (...) which shaped Turing’s work. Beginning with a Moral Sciences Club talk in 1933, Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role. This may be seen not only in “On Computable Numbers” and Turing’s dissertation ), but in his exchanges with Wittgenstein in 1939 and in two later papers, “The Reform of Mathematical Phraseology and Notation” and “Solvable and Unsolvable Problems”. (shrink)

In this Interview, Professor Robert B. Brandom answered ten detailed questions about his philosophy of Rational Pragmatism and Semantic Expressivism, grouped into four topics. 1. Metaphysics and Anthropology, 2. Pragmatics and Semantics, 3. Epistemic Expressivism and 4. Philosophy of Logic. With his careful answers Professor Brandom offers many additional insights into his rigorously constructed account of the relationship “between what we say and think, and what we are saying and thinking about” around the human practice of asking for and giving (...) reasons. A final, additional question pointed at a principal motivation for putting together the present issue: how to reconcile Wittgenstein’s assertion that philosophy must not proffer any theories with the very explicit system of explanations Brandom has constructed. This same issue is addressed to some extent already in Professor Brandom’s new article contained in this issue, but his answer, asserting that he does not proffer a theory but only makes explicit what is already there, might be seen as an unambiguous statement of the continuous presence of a contested Wittgensteinian principle in Brandom’s work. (shrink)

This paper, originating from a Wittgenstein conference in Delphi, Greece in June 2001, questions Brandom’s reading of Wittgenstein on “Following a Rule”. For the purpose of our current investigative dispute, it is a very good starting point to draw our attention to some of the vital differences between Wittgenstein’s and Brandom’s approach to the relation between practice and rules that may not be quite as clear at first sight from Brandom’s own writings. This writing maintains that Brandom misconstrues Wittgenstein’s remarks (...) about signposts and Philosophical Investigations §201 with the consequence that his own explications about tacit rules involved in practice seem more Wittgensteinian than they really are. For one, Brandom duplicates Wittgenstein’s requirement of correctness in rule following: “...correctness that consists in following a rule [does not presuppose] correctness that does not.” On the other hand Brandom’s reading makes Wittgenstein’s quietism look like ”a pretext for not doing constructive work”, while Wittgenstein’s point is that there is nothing left to enquire. (shrink)

In this paper, written more than ten years before Making it Explicit, I take a close look at the pivotal role which assertions play in human interactions. Tending a bridge from the Kantian theory of judgements to Dewey’s pragmatic philosophy, with the Fregean notion of conceptual content providing the pillars, and relying on the teachings drawn from the later Wittgenstein’s philosophy as keystones, I begin by questioning the dominant view of representationalism in analytical philosophy after Russell, Carnap and Tarski. It (...) is here that I begin weaving the conceptual network that will eventually blossom into the program of pragmatic rationalism with logical inferentialism and semantic expressivism as pivotal notions, manifest in our game of asking for and giving reasons. It is for these reasons that I agree that a bilingual version of this early piece seems a good starting point for the reflections on what unites and what divides la philosophical visions of Wittgenstein and my own. (shrink)

[ES] Gottlob Frege posiblemente era el primer filósofo analítico. La exégesis de su doctrina quedó durante varias décadas restringida casi naturalmente al ámbito de la filosofía analítica y angloparlante. El método que Frege heredó a la filosofía analítica se basa en el análisis abstracto y formal, y la aprehensión de su doctrina se desarrolló bajo el supuesto –tomado casi por autoevidente- que éste método es el único correcto para dar cuenta de los problemas filosóficos más fundamentales, muy particularmente el de (...) desarrollar una teoría de significado. Igualmente se asumía y asume todavía con cierto automatismo que las preocupaciones filosóficas de Frege son fundamentalmente las mismas de la filosofía analítica y las que no caben en este supuesto se desechan fácilmente como anacrónicas o absurdas. Este acercamiento al pensamiento de Frege exclusivamente bajo los supuestos de la filosofía analítica, sus méritos no obstante, no toma en cuenta el ambiente anti-naturalista y neo-kantiano en el cual Frege formó sus convicciones fundamentales. Algunos aspectos contenciosos como, por ejemplo, el principio de contexto, una posible jerarquía de sentidos indirectos o la suposición, casi tácita, de que la doctrina de Frege es una teoría sobre expresiones referenciales, aparecen en una luz diferente si nos damos cuenta de que su intento de construir un sistema es, en cuanto a filosofía, en el fondo una respuesta a problemas que Frege encontró en el sistema de Kant. [EN] Gottlob Frege was quite possibly the first analytical philosopher. For several decades the study of his teachings restricted itself almost naturally to the sphere of analytical and English speaking philosophy. The very method which Frege might have impressed upon analytical philosophy takes off with abstract and formal analysis and the apprehension of his doctrine developed under the assumption –taken to be almost self-evident- that this method is the only one capable of correctly accounting for the most fundamental philosophical problems, especially bringing forth a comprehensive theory of meaning. Hence it was taken for granted with certain automatism that the Frege´s philosophical worries were initially identical in its origins with those of contemporary analytical philosophy and those not amenable to easy adoptions are discharged as absurd anachronisms when viewed against current doctrines. Approaching Fregean thought exclusively under the assumptions of analytical philosophy, while having merit, does not take into account the anti-naturalist and neo-Kantian background which influenced the modelling of Frege’s fundamental convictions. Some contentious aspects like for example the context principle, a possible hierarchy of indirect senses or the almost tacit assumption that Frege’s doctrine is a theory about referential expressions appear in a different light, once we become aware that his attempt at system-construction, as far as it concerns philosophy, is fundamentally an answer to problems which Frege found in Kant’s system. (shrink)

[ES] Las dificultades que ofrece el Tractatus para la interpretación detallada de muchos de sus pasajes consideradas claves, junto con la crítica que su autor ha formulado en su desarrollo filosófico posterior contra algunos aspectos de la visión del lenguaje de su primera obra ha tenido frecuentemente la consecuencia de que los intérpretes pierdan de vista el objetivo general de la obra, y en qué grado la filosofía wittgensteiniana es movida por una misma preocupación filosófica durante toda la vida del (...) pensador austro-británico. Una discusión de los motivos de la distinción clave del Tractatus entre lo que dicen y lo que muestran las oraciones sugiere que la visión que motiva esta distinción tractariana sigue vigente en la filosofía posterior de Wittgenstein. [EN] The difficulties encountered for a detailed interpretation of many a key passage of the Tractatus, together with the critical comments the author himself has leveled during his later philosophical development at some aspects of the vision of language in his first opus frequently has had the consequence that some interpreters lose sight of the general target of the work and the degree to which Wittgensteinian philosophy is moved by one and the same philosophical worries during the whole life of the austro-british thinker. An argument of the motives behind the key distinction of the Tractatus between what a proposition says and what it shows suggests that the vision that is the source of this tractarian distinction is forcefully at work also in the later philosophy of Wittgenstein. (shrink)

Las dificultades que ofrece el Tractatus para la interpretación detallada de muchos de sus pasajes considerados clave, junto con la crítica que su autor ha formulado en su desarrollo filosófico posterior contra algunos aspectos de la visión del lenguaje de su primera obra, han tenido frecuentemente como consecuencia que los intérpretes pierdan de vista el objetivo general de la obra, y en qué grado la filosofía wittgensteiniana es movida por una misma preocupación filosófica durante toda la vida del pensador austrobritánico. (...) Una discusión de las causas de la distinción clave del Tractatus entre lo que dicen y lo que muestran las oraciones sugiere que la visión que motiva esta distinción tractariana sigue vigente en la filosofía posterior de Wittgenstein. (shrink)

[ES] El logicismo de Frege o, en términos más generales, su esfuerzo por construir un fundamento de razonamiento deductivo para las matemáticas fue motivado por el deseo de combatir el empirismo radical que empezaba a dominar la discusión científica en las tierras de habla alemana después de la muerte de Hegel. El objetivo similar de Russell unas décadas después, en cambio, se debe en su origen preponderantemente al deseo de superar el neohegelianismo de Bradley. El joven Wittgenstein formuló a partir (...) de lo que aprendió de ambos el sistema del Tractatus, rechazando algunos aspectos claves de uno y otro. Hay, por consiguiente, incompatibilidades importantes entre las tres propuestas de solución para los problemas relacionados con el concepto de la verdad y de la relación que debemos suponer que existe entre mundo, lenguaje y pensamiento. Si sus reflexiones se comparan con el manejo de preguntas aproximadamente equivalentes hoy en día, en particular a raíz del concepto semántico de la verdad que debemos a Tarski, nos podemos dar cuenta que hemos logrado una enorme flexibilidad en el manejo de los lenguajes simbólicos; a este dominio técnico de las herramientas que nos dio la formalización de la lógica simbólica debemos, entre otros avances, el Internet y los teléfonos inteligentes. En cambio, se perdió de vista la profundidad filosófica que estuvo en su origen, y, se podría decir, algo de lo filosófico de la filosofía. El brillo intenso de las tecnologías nuevas junto con la sensación de que tenemos a nuestra disposición una jerarquía infinita de lenguajes o metalenguajes, que nos permiten manejar cualquier problema heredado del nivel anterior, hacen que nos parezca superflua la ocupación con cuestiones más propiamente filosóficas como las entendían los primeros proponentes de la filosofía analítica. Es en parte a esta pérdida de sentido filosófico del quehacer del filósofo que se deben otros fenómenos que hablan de la trivialización de la filosofía: someter esta actividad en el marco académico a una medición cuantitativa que produce un diluvio de trabajos perfectamente inútiles, o la confusión de la filosofía con la elaboración de reglas operativas para hospitales. [EN] Frege’s logicism or, more generally, his efforts to construct a foundation for mathematics based on deductive reasoning was motivated by his wish to fight the radical empiricism that began to dominate scientific argument in German speaking countries after Hegel’s death. Russell’s similar purpose a few decades later, on the other hand, was originally due mainly to their wish to overcome Bradley’s neo-Hegelianism. Young Wittgenstein forged the system of the Tractatus drawing from his knowledge of both, refuting some key aspects of one or other. There are therefore important incompatibilities between the three proposed solutions for the problems related to the concept of truth and to the relation we must suppose exists between world, language and thought. When we compare their thoughts to today’s ways of handling questions which are approximately equivalent, particularly in the wake of the semantic concept of truth we owe to Tarksi, we may become aware that we have certainly gained enormous flexibility in the handling of symbolic languages; the Internet and intelligent telephones, among other signs of progress would have been impossible without this technical mastery of tools we obtained thanks to the formalization of symbolic logic. But, on the other hand, we also lost view of the philosophical depth that stood at its cradle and, it might be said, a bit of what makes philosophy philosophical. The intense sparkle of the new technologies together with the impression that we have an infinite hierarchy of languages or metalanguages at our disposal which allow us to handle any problem inherited from the previous level, may give us the impression that questions related to more deeply philosophical problems, such as the first proponents of analytical philosophy tried to deal with, are idle. Other phenomena which bear witness to the trivialization of philosophy are in part due to this loss of philosophical meaning of the business of philosophy: subduing this activity within the academic framework to methods of quantification which result in a deluge of perfectly useless publications, or the confusion of philosophy with the elaboration of operating rules for hospitals. (shrink)

[ES] La teoría de modelos parte generalmente de la definición de consecuencia lógica ofrecida por Tarski en 1936. John Etchemendy asevera que esta definición contiene una falacia si se le toma como definición genuina de este concepto. Esta aseveración ha desatado una polémica interesante. El presente ensayo resume los puntos principales en discusión y sugiere en su conclusión que el rechazo de la propuesta de Etchemendy se basa en un malentendido de la intención de su crítica, cuyo objeto no es, (...) propiamente dicho, la definición de Tarski, sino que ésta ofrece un fundamento insuficiente para la teoría de modelos. [EN] Model Theory generally assumes the definition of logical consequence proffered by Tarski in 1936. John Etchemendy suggests that Tarski’s definition contains a fallacy, from which an interesting controversy ensued about the definition and its meaning. The main points in discussion are summarized and it is suggested that the controversy is based on a misunderstanding of the intentions of Etchemendy’s criticism: the target is not so much Tarski’s definition, but that it offers an insufficient foundation for Model Theory. (shrink)

[ES] El principio de contexto que Frege establece en Fundamentos de la Aritmética no reaparece en sus escritos posteriores, hecho que podría sugerir que a consecuencia de la sustitución de la noción de contenido juzgable por las de sentido y significado Frege lo rechazara después de 1890. Dummett arguye en 1995 que el principio de contexto continúa formando una parte central de la filosofía de lenguaje de Frege, pero que las teorías establecidas a partir del tomo I de Leyes fundamentales (...) de la aritmética ya no son compatibles con la noción de la perspectiva internalista atribuida a Frege por van Heijenoort e Hintikka. El presente trabajo arguye que Frege no sólo jamás abandonó el principio de contexto, sino que también mantuvo toda su vida la fe en el lenguaje como medio universal con la consiguiente imposibilidad de establecer, vía una teoría semántica, externamente las referencias de nuestros términos. [EN] Frege´s context principle, as put forward in Foundations of Arithmetic, is not mentioned in his later writings which might suggest that as a consequence of substituting the notion of judgeable content by sense and meaning, Frege would have abandoned the context principle after 1890. Dummett argues in 1993 that the context principle continues to form a central part of Frege’s language philosophy; theories put forth from volume I of Fundamental Laws of Arithmetic, however, are no longer compatible with the notion of an internalist perspective attributed to Frege by van Heijenoort and Hintikka. I argue currently that Frege not only never abandoned the context principle but all his life maintained his faith en language as universal medium making and therefore held it impossible to establish reference for our terms externally by means of a theory of meaning. (shrink)