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.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.Shrader-Frechette, Kristine. Tainted: How Philosophy of Science can expose bad science2014, Oxford University Press USA.-
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Added by: Laura Jimenez
Abstract: Lawyers often work pro bono to liberate death-row inmates from flawed legal verdicts that otherwise would kill them. This is the first book on practical philosophy of science, how to practically evaluate scientific findings with life-and-death consequences. Showing how to uncover scores of scientific flaws - typically used by special interests who try to justify their pollution - this book aims to liberate many potential victims of environmentally induced disease and death.It shows how citizens can help uncover flawed science and thus liberate people from science-related societal harms such as pesticides, waste dumps, and nuclear power. It shows how flawed biology, economics, hydrogeology, physics, statistics, and toxicology are misused in ways that make life-and-death differences for humans. It thus analyzes science at the heart of contemporary controversies - from cell phones, climate change, and contraceptives, to plastic food containers and radioactive waste facilities. It illustrates how to evaluate these scientific findings, instead of merely describing what they are. Practical evaluation of science is important because, at least in the United States, 75 percent of all science is funded by special interests, to achieve specific practical goals, such as developing pharmaceuticals or showing some pollutant causes no harm. Of the remaining 25 percent of US science funding, more than half addresses military goals. This means that less than one-eighth of US science funding is for basic science; roughly seven-eighths is done by special interests, for practical projects from which they hope to profit. The problem, however, is that often this flawed, special-interest science harms the public.Comment : Recommended for students in philosophy of science, environmental ethics or science policy. Could serve as an introductory reading for practical philosophy of science. It is easy to read and suitable for undergraduate students.Thalos, Mariam. Explanation is a genus: An essay on the varieties of scientific explanation2002, Synthese 130(3): 317-354.-
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Added by: Nick Novelli
Abstract: I shall endeavor to show that every physical theory since Newton explainswithout drawing attention to causes-that, in other words, physical theories as physical theories aspire to explain under an ideal quite distinctfrom that of causal explanation. If I am right, then even if sometimes theexplanations achieved by a physical theory are not in violation ofthe standard of causal explanation, this is purely an accident. For physicaltheories, as I will show, do not, as such, aim at accommodating the goals oraspirations of causal explanation. This will serve as the founding insightfor a new theory of explanation, which will itself serve as the cornerstoneof a new theory of scientific method.Comment : A striking argument that science does not employ causal explanations. Since this is a commonly-held assumption, this would be interesting to present in the context of scientific methodology, or in an exploration of causation as part of a challenge to whether the idea of causation is actually useful or necessary. Provides good historical context to support its claims. Best taught at an advanced or graduate level.- 1
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