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.
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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.Franklin, L. R.. Exploratory Experiments2005, Philosophy of Science 72(5): 888-899.-
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Added by: Nick Novelli
Abstract: Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.Comment: Good exploration of the role of experiments, challenging the idea that they are solely useful for testing clearly defined hypotheses. Uses many practical examples, but is very concise and clear. Suitable for undergraduate teaching in an examination of scientific methods in a philosophy of science course.
Parke, Emily. Experiments, Simulations, and Epistemic Privilege2014, Philosophy of Science 81(4): 516-536.-
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Added by: Nick Novelli
Abstract: Experiments are commonly thought to have epistemic privilege over simulations. Two ideas underpin this belief: first, experiments generate greater inferential power than simulations, and second, simulations cannot surprise us the way experiments can. In this article I argue that neither of these claims is true of experiments versus simulations in general. We should give up the common practice of resting in-principle judgments about the epistemic value of cases of scientific inquiry on whether we classify those cases as experiments or simulations, per se. To the extent that either methodology puts researchers in a privileged epistemic position, this is context sensitive.Comment: Valuable in raising questions about preconceptions of "science experiments". This article would be useful as part of a look at scientific methodology and the real value obtained from our scientific practices.
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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.