Baker, A. The myth of the seven. To our knowledge, a discussion of these interconnected topics in the form of a special issue was still missing from major philosophical journals. Pincock, C. (2014). Usually, although it needs not be so, these claims bear upon, respectively, the theorems of well-established, fruitful and consistent mathematical theories, and the objects that the terms occurring in these theorems denote when read at face value. Oxford: Oxford University Press.
), Physicalism in mathematics (pp. However, should this route be followed, the notion of the explanatory power of mathematics would lose its ontological import and, pace platonists, could not be used in the Enhanced Indispensability Argument. In the twentieth century, Paul Benacerraf has voiced it in a now famous and clear-cut way (Benacerraf 1973). The papers collected in this special issue are all concerned with debates that have been, however sketchily, touched upon in the previous sections. Panza and Sereni suggest that the currently available versions of such arguments rest on controversial or question-begging assumptions. Mathematical explanation.
Liggins offers a general analysis of how “quantitative relations” may obtain. 515–525; reprinted in Kurt Gödel: Collected works, Vol.
The American Mathematical Monthly, 54, pp. Abstract ‘Indispensability’ is the central concept underpinning the treatment of refusal to deal claims under Article 102 TFEU. Mind, 111(441), 69–74.
Part of Springer Nature.
Many scientific realists usually resort to a causal criterion when arguing in favour of their commitment to physical unobservables (see Cartwright 1983; Hacking 1983; Salmon 1984; Giere 1988), thus placing a causal constraint on such inferences that, clearly, may not be satisfied in the context of mathematical explanations. 88–115). Inference to the best explanation is widely used in philosophy of science, chiefly by those scientific realists who believe scientific theories provide literally true, although approximate, descriptions of the physical world, even in its unobservable parts. (2015). This article is also available for rental through DeepDyve. Register, Oxford University Press is a department of the University of Oxford.
Please check your email address / username and password and try again. Mathematics and scientific representation. PubMed Google Scholar.
Depending on how condition A, i.e. The myth of the seven. doi:10.1093/obo/9780195396577-0029. (1969). they must themselves offer the best explanation of some empirical phenomena (Baker 2009). Colyvan, M. (2010). Theoria—An International Journal for Theory, History and Foundations of Science, 80, 223–242.
Pincock, C. (2004). The indispensability threshold is difficult to meet in practice. 258–276 (1st ed.)
London: Longmans. Sereni then objects that Molinini’s pluralistic proposal may fail to evaluate the advantages of explanations across different contexts. Even though we cannot acknowledge direct access to mathematical abstract objects, it might be enough if we can show that knowledge of the truth of mathematical statements (and of the abstract objects they are about) can somehow be traced back, even indirectly, to knowledge of the truth of empirical statements (and of the concrete objects they are about). To purchase short term access, please sign in to your Oxford Academic account above.
The scope and language of science. Quine, W. V. O.
Oxford Bibliographies in Philosophy. Since its adoption in Magill and Bronner, however, the conventional wisdom that instances of refusal to deal constitute an abuse only in the presence of indispensability has been challenged from multiple directions.
Two physical entities compete in a strong sense when they are logically contradictory; they compete in a weak sense when they undermine the probable existence of each other.
Summing up, claims that indispensability should be an element of the legal test are only credible and relevant where there is vertical integration and the concern relates to the supply of an input (tangible or intangible) or to access to a platform (again, tangible, or intangible).
145–168. These papers are the first explicit contributions to the study of the nature of mathematical explanation in analytic philosophy; with his original account of mathematical explanations in science and in mathematics, Steiner gave a fresh spin to the philosophical discussion.
Mathematical explanation and indispensability arguments.
Benacerraf, P. (1973). (2013). (1980). In “Comments on ‘Parsimony and inference to the best mathematical explanation’,” Fabrice Pataut objects that if proofs must play a theoretical role in explanations that are able to answer why-type questions—say why prime periods are uniquely optimal in Baker’s Magicicada case—it is nevertheless impossible to fix a principled limit to the additional mathematical apparatus one might have to appeal to in the carrying out of such proofs. Australasian Journal of Philosophy, 90(3), 559–578.
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