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Added by: Fenner Stanley TanswellAbstract:
The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem.Coliva, Annalisa. Moore and Wittgenstein: Scepticism, Certainty, and Common Sense2010, 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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Secco, Gisele Dalva, Pereira, Luiz Carlos. Proofs Versus Experiments: Wittgensteinian Themes Surrounding the Four-Color Theorem
2017, in How Colours Matter to Philosophy, Marcos Silva (ed.). Springer, Cham.
Comment (from this Blueprint): Secco and Pereira discuss the famous proof of the Four Colour Theorem, which involved the essential use of a computer to check a huge number of combinations. They look at whether this constitutes a real proof or whether it is more akin to a mathematical experiment, a distinction that they draw from Wittgenstein.