Abstract
As an alternative to the fundamentalist view of nature and science, Nancy Cartwright has developed the view of a patchwork of laws. This paper is not so much concerned with an evaluation of this alternative view as with an account of scientific reasoning with patchworks of laws. Such an account will be given using a modular semantics for axiomatic theories. This semantics, in turn, draws on the framework of partial structures by da Costa and French and a few elements of the Sneed formalism, also known as the structuralist approach to science.
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Notes
- 1.
For a fine-grained account and a classification of ceteris paribus laws, see Schurz (2002).
- 2.
Partiality of a relation R k is more precisely accounted for by distinguishing between the positive extension R k +, the negative extension R k −, and the neutral extension R k 0. For simplicity, we assume that, for any partial structure \(\mathcal{A}\), \(R_{k}^{+} = R_{k}\) and \(R_{k}^{-} =\emptyset\). That is, for any partial structure \(\mathcal{A}\) and any n-ary relation R k , if an n-tuple x is not a member of \(R_{k} = R_{k}^{+}\), it is not a member of R k − either. On this assumption, there is no need to notationally distinguish between the positive, the negative, and the neutral extension of a relation R k in a partial structure.
- 3.
There is no room here for elaborating the distinction between phenomenal and theoretical concepts. I suggest understanding this distinction in a strictly relativised way. See Andreas (2013) for details.
- 4.
That is, in our semantics, a law is true in a subdomain if it is consistently applied there, even if the satisfaction of the consistency requirement does escape our recognition, so that we may fail to see the law operating successfully.
- 5.
The selective use of universal axioms is a key idea in various formalisms of nonmonotonic reasoning. The present modular semantics draws on Brewka (1991).
- 6.
This also achieved by other systems of nonmonotonic reasoning. So far, however, little research has been done on exploiting such systems for an analysis of scientific reasoning.
References
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Andreas, H. (2015). Patchworks of Laws and Partial Structures. In: Mäki, U., Votsis, I., Ruphy, S., Schurz, G. (eds) Recent Developments in the Philosophy of Science: EPSA13 Helsinki. European Studies in Philosophy of Science, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-23015-3_4
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