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)

Dainton and Robinson’s Companion traces lines of descent of analytic philosophy from ancestors. They characterize analytic philosophy as a movement, a tradition, a style, and a commitment to the va...

Gregory Landini offers a new and an illuminating reading of Ludwig Wittgenstein’s idea about his own innovation: it is the invention of a notation that removes the mystery from all theorems of logic and of mathematics as it renders their proofs part of their wordings. This makes all theorems in principle as boring as “all four-legged animals are animals.” This idea is Wittgenstein’s doctrine of showing. It is worthless; yet, as Landini shows, every time Wittgenstein offered an elaboration on it, (...) Russell checked it carefully and found it of no value. This, let me add, shows that Russell was in error in suggesting that intellectually there is no “advantage of theft over honest toil”: at times one may pay back and with high interest. Other cases may be due to misjudgment rather than to sloth. (shrink)

This dissertation presents a philosophical inquiry into the concept of intelligence by reconstructing John Dewey’s theory of intelligence and investigating its educational implications. It presents three critiques of educational practices and theories that, from a Deweyan point of view, are built on misconceptions or oversimplifications of intelligence. While his theory of intelligence is primarily expressed in implicit terms, it offers a nuanced analysis of the sociality and contextuality of intelligence, questioning some of its traditional or mainstream conceptions. The reconstructed theory (...) presented in this dissertation implies that rather than holding onto the idea of individual intelligence, education (and those who are being educated) might benefit from focusing on the social practices and contexts that enable intelligence. The contextuality of intelligence suggests that conceiving intelligence as something that can be universalized, abstracted, and then redistributed is problematic. Dewey’s theory also suggests that people are rich with experience-based contextualized intelligence. To make the most of this, education needs to provide people with a robust theory of knowledge and an aspiration to be informed about the world in multiple and diverse ways. Learning the habit and processes of different kinds of inquiries could benefit societies by contributing to creative and intelligent democratic problem-solving in the inevitably unknown contexts of the future. (shrink)

Charles Sanders Peirce was one of the United States’ most original and profound thinkers, and a prolific writer. Peirce’s game theory-based approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a toolkit for contemporary scholars and philosophers. Drawing on unpublished manuscripts, the book offers a rich, fresh picture of the achievements of a remarkable man.

This monograph proposes a new way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning (...) studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor. The second part of the volume deliberates on the system of correlational inferences by indication and resemblance. The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general. (shrink)

La discussion sur le langage privé que l’on trouve dans les Recherchesphilosophiques a été écrite entre 1937 et 1945, après que les 190 premières remarques de la partie I du livre eurent presque atteint leur forme finale. Les textes post-1936 sur le langage privé constituent un nouveau départ, dans sa lettre et son esprit, par rapport au matériau d’avant 1936.Néanmoins, entre 1929 et 1936, Wittgenstein s’est penché à plusieurs reprises sur l’idée d’un langage « que moi seul peux comprendre ». (...) Un volet de cette question qui, lui, est abordé directement dans les Recherches, c’est l’idée que « si j’appliquais le mot “douleur” uniquement à ce que j’ai nommé jusqu’ici “ma douleur”, et les autres “la douleur de L.W.”, je ne ferais ainsi aucun tort aux autres, si toutefois l’on avait prévu une notation qui d’une façon ou d’une autre, permettrait de pallier l’absence du mot “douleur” dans d’autres combinaisons ». Cependant, la discussion de cette question dans les Recherches est beaucoup plus brève que dans les textes d’avant 1936. J’examine le rapport entre ce § 403 des Recherches d’un côté, et de l’autre côté les textes des cahiers de 1929 et les Remarques philosophiques , en retraçant le développement initial de cette argumentation et en explorant les principales lignes de continuité et de discontinuité dans le traitement que Wittgenstein réserve à la question du langage privé.The discussion of private language in the Investigations was written between 1937 and 1945, after the first 190 remarks of Part I of the book had almost reached their final form. The post-1936 writing on private language represents a fresh start, both in wording and in conception, on the pre-1936 material.Nevertheless, Wittgenstein did repeatedly discuss the idea of a language which “only I myself can understand” during 1929-36. One strand in this discussion that is directly taken up in the Investigations is the idea that “If I were to reserve the word ‘pain’ solely for what I had hitherto called ‘my pain”, and others “L.W.’s pain,” I should do other people no injustice, so long as a notation were provided in which the loss of the word ‘pain’ in other connexions were somehow supplied.” However, the discussion of this topic in the Investigations is much briefer than in the pre-1936 writing. I look at the relationship between §403 and texts from the 1929 notebooks and the Philosophical Remarks, assembled in the spring of 1930, mapping out the earlier development of this line of argument and exploring the principal continuities and discontinuities in Wittgenstein’s treatment of private language. (shrink)

The paper discusses the relation between chess and philosophy, examining, among other things, how far chess might reveal important features of philosophical problemanalysis and argumentation. There is a plurality of scientific, philosophical, and other perspectives from which chess can be viewed. Some attention must be drawn to these various ways of conceptualizing the game, but the main emphasis of the paper lies in uncovering certain philosophically- and metaphilosophically- relevant basic assumptions of chess. It is argued that the thought patterns and (...) reasoning procedures typical of chess seem to merge into those practised in philosophy. Moreover, we face in the common area of chess and other disciplines a multifarious possibility of research programmes, which promise to turn out useful both for the scientific and aesthetic understanding, and perhaps also for the chess tournament practice. Certain philosophical insights inspired by the practice of chess may lead us to transform our views about various complex human phenomena: not only about the nature of calculatory problem-solving and the relation between human intelligence and artificial intelligence, but also about ethical reasoning and even philosophical argumentation itself. (shrink)

Wittgenstein’s language games can be put into a wider service by virtue of elements they share with some contemporary opinions concerning logic and the semantics of computation. I will give two examples: manifestations of language games and their possible variations in logical studies, and their role in some of the recent developments in computer science. It turns out that the current paradigm of computation that Girard termed Ludics bears a striking resemblance to members of language games. Moreover, the kind of (...) interrelations that are emerging could be scrutinised from the viewpoint of logic that virtually necessitates game-theoretic conceptualisations, demonstrating the fact that the meaning of utterances may, in many situations, be understood as Wittgenstein’s language games of ‘showing or telling what one sees’. This provides motivation for the use of games in relation to logic and formal semantics that some commentators have called for. Many of the ideas can be traced to C.S. Peirce, for whom signs were vehicles of strategic communication. The conclusion about Wittgenstein is that the notions of saying and showing converge in his late philosophy. (shrink)

This article discusses Jaakko Hintikka's interpretation of the aims and method of Husserl's phenomenology. I argue that Hintikka misrepresents Husserl's phenomenology on certain crucial points. More specifically, Hintikka misconstrues Husserl's notion of "immediate experience" and consequently fails to grasp the functions of the central methodological tools known as the "epoché" and the "phenomenological reduction." The result is that the conception of phenomenology he attributes to Husserl is very far from realizing the philosophical potential of Husserl's position. Hence if we want (...) a fruitful rapprochement between analytical philosophy and Continental phenomenology of the kind that is Hintikka's ultimate aim, then Hintikka's account of Husserl needs correcting on a number of crucial points. (shrink)

Les Remarques philosophiques sont la première tentative de mettre en oeuvre le programme qui découle de l’échec du projet du Tractatus Logico-Philosophicus. Le noyau de ce programme est donné par l’abandon de l’analyse des nombres avancée dans le Tractatus. Wittgenstein se rend compte que les nombres doivent se trouver à la base même du langage, dans la structure des propositions élémentaires. En même temps, il se rend compte qu’il est impossible de fournir la logique sousjacente au langage avant d’avoir procédé (...) à l’analyse. Le projet d’une investigation logique des phénomènes s’imposait, donc, même après l’abandon de l’idée d’un langage phénoménologique. The Philosophical Remarks is a first attempt at pursuing the philosophical agenda determined by the failure of the Tractarian project. The central point of this agenda is the abandonment of the analysis of number that had been given in the Tractatus. Wittgenstein realizes that numbers should be brought back to the basis of language, as part of the structure of the elementary propositions themselves. At the same time, he realizes that it is impossible to give the logic underlying our language before the process of logical analysis is carried out. He undertakes the project of a logical investigation of phenomena even after giving up the idea of a phenomenological language. (shrink)

The standard approach to model how human beings understand natural languages is the symbolic, compositional approach according to which the meaning of a complex expression is a function of the meanings of its constituents. In other words, meaning plays a fundamental role in the model. In this work, because of the polysemous, flexible, dynamic, and contextual structure of natural languages, this approach is rejected. Instead, a connectionist model which eliminates the concept of meaning is proposed.