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Coliva, Annalisa. Extended Rationality: A Hinge Epistemology
2015, Basingstoke: Palgrave Macmillan.
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Added by: Jie Gao
Publisher's Note: Extended Rationality: A Hinge Epistemology provides a novel account of the structure of epistemic justification. Its central claim builds upon Wittgenstein's idea in On Certainty that epistemic justifications hinge on some basic assumptions and that epistemic rationality extends to these very hinges. It exploits these ideas to address major problems in epistemology, such as the nature of perceptual justifications, external world skepticism, epistemic relativism, the epistemic status of basic logical laws, of the Principle of the Uniformity of Nature, of our belief in the existence of the past and of other minds, and the nature of testimonial justification. Along the way, further technical issues, such as the scope of the Principle of Closure of epistemic operators under known entailment, the notion of transmission failure, and the existence of entitlements are addressed in new and illuminating ways.

Comment: In this interesting book, Annalisa Coliva develops an account of the structure of justification inspired by Wittgenstein's epistemology (Ch.1-3), argues a constitutivism about epistemic rationality (Ch.4) and reveals its significance for many contemporary problems (Ch.5). Ch.1 involves a overview of three dominant views of perceptual warrants: liberalism, conservativism and moderatism, so it could be a useful reading material for teachings on epistemic justification and perceptual warrant. Ch.4 can be used as a further reading for topics on epistemic rationality, Wittgenstein's epistemology and external world skepticism.

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Coliva, Annalisa. Moore and Wittgenstein: Scepticism, Certainty, and Common Sense
2010, Basingstoke: Palgrave Macmillan.
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Added by: Jie Gao
Publisher's Note: Does scepticism threaten our common sense picture of the world? Does it really undermine our deep-rooted certainties? This book offers an answer to these questions through a comparative study of the epistemological work of two key figures in the history of analytic philosophy: G. E. Moore and Ludwig Wittgenstein. While historically accurate and engaging with scholarly work in this area, the book also puts forward novel interpretations of their works and brings out their relevance to present-day debates both in epistemology and philosophy of language.

Comment: This book is a useful and sustained examination of a variety of themes in Wittgenstein's On Certainty, the very late compilation of remarks inspired by G.E. Moore's engagement with scepticism and idealism in "A Defence of Common Sense," "Proof of an External World" and a few other papers. Among the topics considered are the strategies of Moore's arguments, ordinary and philosophical uses of language, differing interpretations of Moore, externalism, internalism and contextualism, Wittgenstein's objections to Moore, meaning and use, language games, Cartesian and Humean sceptical arguments, the epistemic and semantic status of so-called "hinge" propositions, epistemic relativism, and a comparison of Wittgenstein's and Moore's views with those of subsequent philosophers. It thus constitutes a very good reading or even central text for a course on Moore's epistemology, Wittgenstein's epistemology and external world skepticism.

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Francois, Karen, Vandendriessche, Eric. Reassembling Mathematical Practices: a Philosophical-Anthropological Approach
2016, Revista Latinoamericana de Etnomatemática Perspectivas Socioculturales de la Educación Matemática, 9(2): 144-167.
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Added by: Fenner Stanley Tanswell
Abstract: In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.

Comment: Francois and Vandendriessche here present a later Wittgensteinian approach to “ethnomathematics”: mathematics practiced outside of mainstream Western contexts, often focused on indigenous or tribal groups. They focus on two case studies, string-figure making and sand-drawing, in different geographic and cultural contexts, looking at how these practices are mathematical.

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Ruth Garrett Millikan. Truth, Rules, Hoverflies, and the Kripke-Wittgenstein Paradox
1990, Philosophical Review 99 (3):323-53
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Added by: Björn Freter, Contributed by: Hannah Ginsborg

Abstract: "[T]he sceptical argument that Kripke attributes to Wittgenstein, and even the 'sceptical solution', are of considerable importance regardless of whether they are clearly Wittgenstein's. The naturalistically inclined philosopher, who rejects Brentano's irreducibility and yet holds intentionality to be an objective feature of our thoughts, owes a solution to the Kripke-Wittgenstein paradox." The challenge is a welcome one. Although I will argue that the Kripke-Wittgenstein paradox is not a problem for naturalists only, I will propose a naturalist solution to it. (Should the Kripke-Wittgenstein paradox prove to be soluble from a naturalist standpoint but intractable from other standpoints, that would, I suppose, constitute an argument for naturalism.) Then I will show that the paradox and its solution have an important consequence for the theories of meaning and truth. The Kripke-Wittgenstein arguments which pose the paradox also put in question Dummett's and Putnam's view of language understanding. From this view it follows that truth rules must be "verificationist rules" that assign assertability conditions to sentences, rather than "realist rules" that assign correspondence truth conditions. The proposed solution to the paradox suggests another view of language understanding, according to which a speaker can express, through his language practice, a grasp of correspondence truth rules.

Comment: Can be assigned alongside Kripke's *Wittgenstein on Rules and Private Language* as part of an undergraduate course in the theory of meaning or the philosophy of language. Engaging and sparks good discussion.

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