Rules, understanding and language games in mathematics

Mathematical Practice ◽

Language Game ◽

Language Games ◽

Logical Necessity ◽

Foundations Of Mathematics ◽

Mathematical Concepts ◽

Form Of Life ◽

Inherent Ambiguity

The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the community, as well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games.

Forms of Life

Nordic Wittgenstein Review ◽

10.15845/nwr.v4i0.3320 ◽

2015 ◽

pp. 1 ◽

Cited By ~ 4

Author(s):

Peter Hacker

Keyword(s):

Philosophy Of Language ◽

Language Games ◽

Truth Conditions ◽

Form Of Life ◽

Transformation Rules ◽

Forms Of Life ◽

A Minor ◽

Varied History

The phrase ‘Lebensform’ (form of life) had a long and varied history prior to Wittgenstein’s use of it on a mere three occasions in the Philosophical Investigations. It is not a pivotal concept in Wittgenstein’s philosophy. But it is a minor signpost of a major reorientation of philosophy, philosophy of language and logic, and philosophy of mathematics that Wittgenstein instigated. For Wittgenstein sought to replace the conception of a language as a meaning calculus (Frege, Russell, the Tractatus) by an anthropological or ethnological conception. A language is not a class of sentences that can be formed from a set of axioms (definitions), formation and transformation rules and the meanings of which is given by their truth-conditions, but an open-ended series of interlocking language-games constituting a form of life or way of living (a culture). Wittgenstein’s uses of ‘Lebensform’ and its cognates, both in the Investigations and in his Nachlass are severally analysed, and various exegetical misinterpretations are clarified.

Playing ethics and teaching morality: how wittgenstein could help us to apply games to the moral living

Trans/Form/Ação ◽

10.1590/s0101-31732017000400006 ◽

2017 ◽

Vol 40 (4) ◽

pp. 89-110

Author(s):

Janyne Sattler

Keyword(s):

Language Game ◽

Moral Judgments ◽

Human Communication ◽

Human Form ◽

Moral Language ◽

Learning And Teaching ◽

Form Of Life ◽

Moral Engagement

ABSTRACT: In Wittgenstein's Philosophical Investigations the notion of a 'language game' gives human communication a regained flexibility. Contrary to the Tractatus, the ethical domain now composes one language game among others, being expressed in various types of sentences such as moral judgments, imperatives and praises, and being shared in activity by a human form of life. The aim of this paper is to show that the same moves that allow for a moral language game are the ones allowing for learning and teaching about the moral living, where persuasion takes the place of argument by means of a plural appeal. For this purpose, literature would seem to be one of the best tools at our disposal. As a way of exemplifying our moral engagement to literature I proceed at last to a brief analysis of Tolstoy's Father Sergius, to show how playing this game would help us accomplish this pedagogical enterprise.

"Let us imagine...": Wittgenstein's Invitation to Philosophy

Nordic Wittgenstein Review ◽

10.15845/nwr.v4i2.3292 ◽

2015 ◽

pp. 99-115

Author(s):

Beth Savickey

Keyword(s):

Language Game ◽

Language Games ◽

Social Psychological ◽

Form Of Life ◽

Constitutive Relationships ◽

The Social ◽

Power And Authority

Wendy Lee-Lampshire writes that Wittgenstein’s conception of language has something valuable to offer feminist attempts to construct epistemologies firmly rooted in the social, psychological and physical situations of language users (1999: 409). However, she also argues that his own use of language exemplifies a form of life whose constitutive relationships are enmeshed in forms of power and authority. For example, she interprets the language game of the builders as one of slavery, and questions how we read and respond to it. She asks: “Who are ‘we’ as Wittgenstein’s reader(s)?” This is an important question, and how we answer offers insight not only into our own philosophical practices, but also into Wittgenstein’s use of language games. With the words “Let us imagine...”, Wittgenstein invites readers to participate in creative, collaborative, and improvisational language games that alter not only the texts themselves, but our relationship with others.

Wittgenstein on ethics: Working through Lebensformen

Philosophy & Social Criticism ◽

10.1177/0191453718810918 ◽

2020 ◽

Vol 46 (2) ◽

pp. 115-130 ◽

Cited By ~ 1

Author(s):

Juliet Floyd

Keyword(s):

Subject Matter ◽

Language Game ◽

Philosophical Method ◽

Form Of Life ◽

Working Through ◽

Significant Step

In his Tractatus Logico-Philosophicus, Wittgenstein conveyed the idea that ethics cannot be located in an object or self-standing subject matter of propositional discourse, true or false. At the same time, he took his work to have an eminently ethical purpose, and his attitude was not that of the emotivist. The trajectory of this conception of the normativity of philosophy as it developed in his subsequent thought is traced. It is explained that and how the notion of a ‘form of life’ ( Lebensform) emerged only in his later thought, in 1937, earmarking a significant step forward in his philosophical method. We argue that the concept of Lebensform represents a way of domesticating logic itself, the very idea of a claim or reason, supplementing the idea of a ‘language game’, which it deepens. Lebensform is contrasted with the phenomenologists’ Lebenswelt through a reading of the notions of ‘I’, ‘world’ and ‘self’ as they were treated in the Tractatus, The Blue and Brown Books and Philosophical Investigations. Finally, the notion of Lebensform is shown to have replaced the notion of culture ( Kultur) in Philosophical Investigations. Wittgenstein’s spring 1937 ‘domestication’ of the nature of logic is shown to have been fully consonant with the idea that he was influenced by his reading Alan Turing’s 1936/1937 paper, ‘On computable numbers, with an application to the Entscheidungsproblem’.

Wittgenstein on Mathematical Proof

Royal Institute of Philosophy Supplement ◽

10.1017/s1358246100005257 ◽

1990 ◽

Vol 28 ◽

pp. 79-99 ◽

Cited By ~ 1

Author(s):

Crispin Wright

Keyword(s):

Mathematical Proof ◽

Short Paper ◽

Foundations Of Mathematics ◽

The Real ◽

Philosophical Investigations

To be asked to provide a short paper on Wittgenstein's views on mathematical proof is to be given a tall order (especially if little or no familiarity either with mathematics or with Wittgenstein's philosophy is to be presupposed!). Close to one half of Wittgenstein's writings after 1929 concerned mathematics, and the roots of his discussions, which contain a bewildering variety of underdeveloped and sometimes conflicting suggestions, go deep to some of the most basic and difficult ideas in his later philosophy. So my aims in what follows are forced to be modest. I shall sketch an intuitively attractive philosophy of mathematics and illustrate Wittgenstein's opposition to it. I shall explain why, contrary to what is often supposed, that opposition cannot be fully satisfactorily explained by tracing it back to the discussions of following a rule in the Philosophical Investigations and Remarks on the Foundations of Mathematics. Finally, I shall try to indicate very briefly something of the real motivation for Wittgenstein's more strikingly deflationary suggestions about mathematical proof, and canvass a reason why it may not in the end be possible to uphold them.

Die Gewissheit der Orientierung

Wittgenstein-Studien ◽

10.1515/witt-2019-0003 ◽

2019 ◽

Vol 10 (1) ◽

pp. 37-71

Author(s):

Werner Stegmaier

Keyword(s):

Common Sense ◽

Language Game ◽

External World ◽

Language Games ◽

On Certainty ◽

The Earth ◽

Closing The Gap ◽

New Interpretation

AbstractIn his treatises A Defence of Common Sense (1925), Proof of an External World (1939), and Certainty (1941), G.E. Moore wanted to put an end to the modern doubts about the certainty of reality and the ‘external world’ by pointing to the undeniable plausibilities of ‘empirical propositions,’ such as ‘I know that this is my hand’ or ‘I know that the earth had existed before my body was born.’ Wittgenstein, who was intensely grappling with Moore’s proofs during the last one and a half years before his expected death, still questioned these proofs and countered them with his concept of language games – including a different logic of the ‘connection with reality.’ Philosophically, he thereby left many loose ends in all places and admittedly a ‘gap’ between them, which he was no longer able to close. But he prepared for closing the gap by means of his concept of orientation, which he had initiated in his Philosophical Investigations without defining it in this term. In a new interpretation of On Certainty from the perspective of the Philosophy of Orientation, this paper tries to show how the attention to the phenomenon of orientation and the language game in which it is expressed can close this gap and thus carry on Wittgenstein's late philosophy to a certain point.

Antirealism/realism of Wittgenstein's language-game idea

Papers on Philosophy Psychology Sociology and Pedagogy ◽

10.15291/radovifpsp.2404 ◽

2018 ◽

Vol 27 (4) ◽

Author(s):

Heda Festini

Keyword(s):

Natural History ◽

Language Game ◽

Language Games ◽

General Notion ◽

New Objectivity ◽

Human Reality ◽

Truth Conditional ◽

New Criterion ◽

Methodology Of Science

Wittgenstein’s language-game idea allews/us te find out both, antirealistic and realistic tendencies, what is required te abanden classification an realistic and antirealistic (constructivistic, instrumentalistic) approaches in semantics and methodology of science/that originated in discussions on the philosophy of mathematics. Using some relevant commentators of Wittgenstein’s works (Dummett, Baker, Hintikka, Kiripke. C. Wright etc.) a broader notion of realism will be obtained using the following questions: A. human reality: natural history or forms of life (behaviour, practice, training, customs and institutions — language-games and correct use), B. new objectivity: community, agreement (criterion - following rules), C. the new nuance in the nation of truth: justification, verification (proof as an method of verification). The results of the analysis will be the impontant for a new criterion of realism such as: the general notion of reality, objectivity as intersubjectivity and the nuances in the notion of truth.With the new criterion we have the following map of realism: 1. F-rege-Tarski-Carnap truth-conditional realism, 2. Frege-Wittgenstein justification/verificatdonist realism, 3. Frege-Wittgenstein-Hintikka verificationist/falsificationist realism.The possibility of Frege-Wittgenstein-Dummett neoveificationist realism is open to further research.

Wittgenstein, Translation, and Semiotics

Target ◽

10.1075/target.1.1.06gor ◽

1989 ◽

Vol 1 (1) ◽

pp. 69-94 ◽

Cited By ~ 5

Author(s):

Dinda L. Gorlée

Keyword(s):

Language Game ◽

Language Games ◽

Three Stages

Abstract Wittgenstein discusses interlingual and intersemiotic translation, both in its own right and, more often, as an object of comparison. In his Tractatus Logico-Philosophicus (1922), he puts forth a pictorial view which can be construed in Saussurian terms. This rule-governed notion of translation is, in Wittgenstein's later work, dynamized and based upon the use of signs. Translation is one of the language-games in Philosophical Investigations (1953). Wittgenstein's language-game of translation approaches Peirce's semiosis. Language-games are thirds which, in their nonverbal aspects, also partake of secondness and firstness. The language-game of translation occurs, at least theoretically, in three stages corresponding to the three logical interpretants.

Language Use in Mathematical Practice: An Ethnographic Perspective

Society and Culture in South Asia ◽

10.1177/2393861718767239 ◽

2018 ◽

Vol 4 (2) ◽

pp. 208-232

Author(s):

Saumya Malviya

Keyword(s):

South Asian ◽

Social Practice ◽

Language Use ◽

Mathematical Practice ◽

Two Dimensions ◽

Mathematical Language ◽

Form Of Life ◽

Action Knowledge

Mathematics is often seen as an epitome of cold objectivity and astounding infallibility. Particularly for the outsiders, it comes across as an extremely rigid and closed system which seems impenetrable owing to its very specific and technical language. This article problematises these assumptions and seeks to study mathematics as a social practice with insights drawn from an anthropology of language and concepts, Wittgenstein’s philosophy of mathematics and semiotics. Using the anthropological insight that a language is always embedded in a form of life, this article shows how mathematical practice generates its own conventions and forms of language use. In particular, two dimensions of language use in mathematics are delineated and their consequences for further research are drawn out. In the first part of the article, the role of concepts in the discourse of mathematics is explored and in the second it is shown how applying a rigid distinction between syntax and semantics to mathematical language obstructs our understanding of its fluid and dynamic character. The argument unfolds through an analyses of interviews, texts and classroom sessions and shows how mathematical practice is heavily context bound and mathematicians often display an ethnographic attentiveness towards their work. The general tenor of the description is such that it attempts to trace the ethical dimension latent in mathematical practice and suggests a possibility of exploring it as a form of life. Connected to this thought is the argument that like any other practice, mathematical practice generates its own forms of reflections which cannot simply be assimilated to philosophical/theoretical knowledge. The question whether this action knowledge regarding mathematics has some relation to the South Asian location where the ethnography unfolds is also tentatively explored.

“What belongs to a language game is a whole culture.”

Wittgenstein-Studien ◽

10.1515/witt-2018-0005 ◽

2018 ◽

Vol 9 (1) ◽

pp. 51-73 ◽

Cited By ~ 1

Author(s):

Marco Brusotti

Keyword(s):

First Language ◽

Language Game ◽

Language Games ◽

Cultural Comparison ◽

The West ◽

Aesthetic Judgement ◽

Fourth Section ◽

Form Of Life ◽

Conceptual Connection ◽

Full Reconstruction

Abstract:Wittgenstein remarks that “What belongs to a language game is a whole culture”, and that describing the language games in which the “words we call expressions of aesthetic judgement” are used implies describing “the culture of a period” (LA 1966: 8). Without aiming at a full reconstruction, the paper addresses the gradual emergence of the close conceptual connection between “language game” and “culture” in Wittgenstein’s manuscripts. The apparently obvious idea that “language game” and “form of life” (or “culture”) belong together or even coincide was originally missing. The paper picks out few episodes from Wittgenstein’s philosophical development. The first chapter shows that the topic of cultural diversity emerges in Wittgenstein’s reception of Oswald Spengler’s The Decline of the West, but still plays only a limited role in his first criticism of James Frazer’s The Golden Bough. The second chapter discusses the emergence of the term “language game” and establishes that Wittgenstein’s first language games do not yet imply something like an “anthropological view”. Real and imaginary “peoples” and “tribes” make their first appearance in remarks that ascribe a “primitive” arithmetic to them (chapter 3). Finally, with an eye to the possible influence of Sraffa and Malinowski, the fourth section shows how the Brown Book conceives translation as holistic cultural comparison.